0,3

Sometimes also called lambda numbers.

Also denominators of continued fraction convergents to sqrt(2): 1, 3/2, 7/5, 17/12, 41/29, 99/70, 239/169, 577/408, 1393/985, 3363/2378, 8119/5741, 19601/13860, 47321/33461, 114243/80782, ... = A001333/A000129

Number of lattice paths from (0,0) to the line x=n-1 consisting of U=(1,1), D=(1,-1) and H=(2,0) steps (i.e. left factors of Grand Schroeder paths); for example, a(3)=5, counting the paths H, UD, UU, DU and DD. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 27 2002

a(2*n) with b(2*n) := A001333(2*n), n>=1, give all (positive integer) solutions to Pell equation b^2 - 2*a^2 = +1 (see Emerson reference). a(2*n+1) with b(2*n+1) := A001333(2*n+1), n>=0, give all (positive integer) solutions to Pell equation b^2 - 2*a^2 = -1.

Bisection: a(2*n+1)= T(2*n+1,sqrt(2))/sqrt(2)= A001653(n), n>=0 and a(2*n)= 2*S(n-1,6)= 2*A001109(n),n>=0, with T(n,x), resp. S(n,x), Chebyshev's polynomials of the first,resp. second kind. S(-1,x)=0. See A053120, resp. A049310. - W. Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Jan 10 2003

Consider the mapping f(a/b) = (a + 2b)/(a + b). Taking a = b = 1 to start with and carrying out this mapping repeatedly on each new (reduced) rational number gives the following sequence 1/1, 3/2,7/5,17/12,41/29,... converging to 2^(1/2). Sequence contains the denominators. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Mar 22 2003

This is also the Horadam sequence (0,1,1,2). a(n) / a(n-1) converges to 2^1/2 + 1 as n approaches infinity. - Ross La Haye (rlahaye(AT)new.rr.com), Aug 18 2003

Number of 132-avoiding two-stack sortable permutations.

y satisfying x^2 - 2*y^2=-+1. Corresponding x given by A001333(n). - Lekraj Beedassy (blekraj(AT)yahoo.com), Jun 24 2004

For n>0, the number of (s(0), s(1), ..., s(n)) such that 0 < s(i) < 4 and |s(i) - s(i-1)| <= 1 for i = 1,2,....,n, s(0) = 2, s(n) = 3. - Herbert Kociemba (kociemba(AT)t-online.de), Jun 02 2004

Number of (s(0), s(1), ..., s(n)) such that 0 < s(i) < 4 and |s(i) - s(i-1)| <= 1 for i = 1,2,....,n, s(0) = 1, s(n) = 2. - Herbert Kociemba (kociemba(AT)t-online.de), Jun 02 2004

Counts walks of length n from a vertex of a triangle to another vertex to which a loop has been added. - Mario Catalani (mario.catalani(AT)unito.it), Jul 23 2004

Apart from initial terms, Pisot sequence P(2,5). See A008776 for definition of Pisot sequences. - David W. Wilson (davidwwilson(AT)comcast.net)

Sums of antidiagonals of A038207 [Pascal's triangle squared] - Ross La Haye (rlahaye(AT)new.rr.com), Oct 28 2004

The Pell primality test is "If N is an odd prime, then P(N)-kronecker(2,N) is divisible by N". "Most" composite numbers fail this test, so it makes a useful pseudoprimality test. The odd composite numbers which are Pell pseudoprimes (i.e. that pass the above test) are in A099011. - Jack Brennen (jb(AT)brennen.net), Nov 13, 2004

a(n) = sum of n-th row of triangle in A008288 = A094706(n)+A000079(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Dec 03 2004

Pell trapezoids (cf. A084158); for n>0, A001109(n)= (a(n-1)+a(n+1))*a(n)/2; e.g. 1189=(12+70)*29/2 - Charlie Marion (charliemath(AT)optonline.net), Apr 1 2006

(0!a(1),1!a(2),2!a(3),3!a(4),...) and (1,-2,-2,0,0,0,...) form a reciprocal pair under the list partition transform and associated operations described in A133314. - Tom Copeland (tcjpn(AT)msn.com), Oct 29 2007

Let C = (sqrt(2)+1) = 2.414213562..., then for n>1, C^n = a(n)*(1/C) + a(n+1). Example: C^3 = 14.0710678... = 5*(.414213562...) + 12. Let X = the 2 X 2 matrix [0, 1; 1, 2]; then X^n * [1, 0] = [a(n-1), a(n); a(n), a(n+1)]. a(n) = numerator of n-th convergent to (Sqrt(2)-1) = .41421356... = [2, 2, 2,...], the convergents being [1/2, 2/5, 5/12,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 21 2007

A = sqrt(2) = 2/2 + 2/5 + 2/(5*29) + 2/(29*169) + 2/(169*985) + ...; B = ((5/2) - sqrt(2)) = 2/2 + 2/(2*12) + 2/(12*70) + 2/(70*408) + 2/(408*2378) + ...; A+B = 5/2. C = 1/2 = 2/(1*5) + 2/(2*12) + 2/(5*29) + 2/(12*70) + 2/(29*169) + ... - Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 16 2008

Prime Pell numbers with an odd index gives the RMS value (A141812) of prime RMS numbers (A140480). [From Ctibor O. Zizka (ctibor.zizka(AT)seznam.cz), Aug 13 2008]

Comment from Clark Kimberling (ck6(AT)evansville.edu), Aug 27 2008 (Start): Related convergents (numerator/denominator):

lower principal convergents: A002315/A001653

upper principal convergents: A001541/A001542

intermediate convergents: A052542/A001333

lower intermediate convergents: A005319/A001541

upper intermediate convergents: A075870/A002315

principal and intermediate convergents: A143607/A002965

lower principal and intermediate convergents: A143608/A079496

upper principal and intermediate convergents: A143609/A084068 (End)

Equals row sums of triangle A143808 starting with offset 1. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 01 2008]

Recurrence a(n)=2a(n-1)+a(n-2) holds for b(n)= 1, A000129. [From Paul Curtz (bpcrtz(AT)free.fr), Oct 23 2008]

Binomial transform of the sequence:= 0,1,0,2,0,4,0,8,0,16,..., powers of 2 alternating with zeros. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 28 2008]

a(n) is also the sum of the nth row of the triangle formed by starting with the top two rows of Pascal's triangle and then each next row has a 1 at both ends and the interior values are the sum of the three numbers in the triangle above that position. [From Patrick Costello (pat.costello(AT)eku.edu), Dec 07 2008]

Starting with offset 1 = eigensequence of triangle A135387 (an infinite lower triangular matrix with (2,2,2,...) in the main diagonal and (1,1,1,...) in the subdiagonal. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 29 2008]

Starting with offset 1 = row sums of triangle A153345 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 24 2008]

Contribution from Charlie Marion (charliemath(AT)optonline.net), Jan 07 2009: (Start)

In general, denominators, a(k,n) and numerators, b(k,n), of continued

fraction convergents to sqrt((k+1)/k) may be found as follows:

let a(k,0) = 1, a(k,1) = 2k; for n>0, a(k,2n) = 2*a(k,2n-1)+a(k,2n-2)

and a(k,2n+1)=(2k)*a(k,2n)+a(k,2n-1);

let b(k,0) = 1, b(k,1) = 2k+1; for n>0, b(k,2n) = 2*b(k,2n-1)+b(k,2n-2)

and b(k,2n+1)=(2k)*b(k,2n)+b(k,2n-1).

For example, the convergents to sqrt(2/1) start 1/1, 3/2, 7/5,

17/12, 41/29.

In general, if a(k,n) and b(k,n) are the denominators and numerators,

respectively, of continued fraction convergents to sqrt((k+1)/k)

as defined above, then

k*a(k,2n)^2-a(k,2n-1)*a(k,2n+1)=k=k*a(k,2n-2)*a(k,2n)-a(k,2n-1)^2 and

b(k,2n-1)*b(k,2n+1)-k*b(k,2n)^2=k+1=b(k,2n-1)^2-k*b(k,2n-2)*b(k,2n);

for example, if k=1 and n=3, then a(1,n)=a(n+1) and

1*a(1,6)^2-a(1,5)*a(1,7)=1*169^2-70*408=1;

1*a(1,4)*a(1,6)-a(1,5)^2=1*29*169-70^2=1;

b(1,5)*b(1,7)-1*b(1,6)^2=99*577-1*239^2=2;

b(1,5)^2-1*b(1,4)*b(1,6)=99^2-1*41*239=2.

Cf. A001333, A142238-A142239, A153313-153318.

[From Charlie Marion (charliemath(AT)optonline.net), Jan 07 2009]

(End)

Starting with offset 1 = row sums of triangle A155002, equivalent to the statement that the Fibonacci series convolved with the Pell series prefaced with a "1": (1, 1, 2, 5, 12, 29,...) = (1, 2, 5, 12, 29,...). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 18 2009]

It appears that P(p) == 8^((p-1/2)) mod p, p = prime; analogous to [Schroeder, p.90]: Fp == 5^((p-1)/2)) mod p. Example: Given P(11) = 5741, == 8^5 mod 11. Given P(17) = 11336689, == 8^8 mod 17 since 17 divides (8^8 - P(l7)). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 21 2009]

Equals eigensequence of triangle A154325 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 12 2009]

Another combinatorial interpretation of a(n+1) arises from a simple tiling scenario. Namely, a(n+1) gives the number of ways of tiling a 1 by n rectangle with indistinguishable 1 by 2 rectangles and 1 by 1 squares that come in two varieties, A and B say. For example, with C representing the 1 by 2 rectangle, we obtain a(4)=12 from AAA, AAB, ABA, BAA, ABB, BAB, BBA, BBB, AC, BC, CA and CB. [From Martin Griffiths (griffm(AT)essex.ac.uk), Apr 25 2009]

a(n+1)=2*a(n)+ a(n-1) a(1=1,a(2)=2 was used by Theon from Smyrna. [From Sture Sjoestedt (sture.sjostedt(AT)spray.se), May 29 2009]

P. Bachmann, Niedere Zahlentheorie (1902, 1910), reprinted Chelsea, NY, 1968, vol. 2, p. 76.

Paul Barry, A Catalan Transform and Related Transformations on Integer Sequences, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.5.

Paul Barry, On Integer-Sequence-Based Constructions of Generalized Pascal Triangles, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.4.

A. H. Beiler, Recreations in the Theory of Numbers. New York: Dover, pp. 122-125, 1964.

John Derbyshire, Prime Obsession, Joseph Henry Press, 2004, see p. 16.

E. Deutsch, A formula for the Pell numbers, Problem 10663, Amer. Math. Monthly 107 (No. 4, 2000), solutions pp. 370-371.

E. I. Emerson, Recurrent sequences in the equation DQ^2=R^2+N, Fib. Quart., 7 (1969), 231-242, Ex.1, p. 237-8.

S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 1.1.

A. F. Horadam, Special Properties of the Sequence W(n){a, b; p, q}, Fibonacci Quarterly, Vol. 5, No. 5, 1967, pp. 424-434.

A. F. Horadam, Pell identities, Fib. Quart., 9 (1971), 245-252, 263.

Problem B-82, Fib. Quart., 4 (1966), 374-375.

P. Ribenboim, The Book of Prime Number Records. Springer-Verlag, NY, 2nd ed., 1989, p. 43.

J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 224.

Ayoub B. Ayoub, "Fibonacci-like sequences and Pell equations", The College Mathematics Journal, Vol. 38 (2007), pp. 49-53.

Clark Kimberling, "Best lower and upper approximates to irrational numbers," Elemente der Mathematik, 52 (1997) 122-126.

Serge Lang, Introduction to Diophantine Approximations, Addison-Wesley, New York, 1966.

Hao Pan, Arithmetic properties of q-Fibonacci numbers and q-Pell numbers, Discr. Math., 306 (2006), 2118-2127. [From N. J. A. Sloane (njas(AT)research.att.com), Jan 29 2009]

Manfred R. Schroeder, "Number Theory in Science and Communication", 5-th ed., Springer-Verlag, 2009, p. 90. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 21 2009]

Mark A. Shattuck, Tiling proofs of some formulas for the Pell numbers of odd index, Integers, 9 (2009), 53-64.

Extending Theons Ladder to Any Square Root Problem 3858 in Elementa nr4 1996 [From Sture Sjoestedt (sture.sjostedt(AT)spray.se), May 29 2009]

N. J. A. Sloane, Table of n, a(n) for n = 0..500

Joerg Arndt, Fxtbook

Tewodros Amdeberhan, Solution to problem #10663 (AMM)

P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.

E. S. Egge and T. Mansour, 132-avoiding two-stack sortable permutations....

Nick Hobson, Python program for this sequence

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 135

Tanya Khovanova, Recursive Sequences

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

James A. Sellers, Domino Tilings and Products of Fibonacci and Pell Numbers, Journal of Integer Sequences, Vol. 5 (2002), Article 02.1.2

R. A. Sulanke, Moments, Narayana numbers and the cut and paste for lattice paths

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Eric Weisstein's World of Mathematics, Pythagoras's Constant

Eric Weisstein's World of Mathematics, Square Triangular Number

Index entries for "core" sequences

Index entries for sequences related to Chebyshev polynomials.

Index entries for sequences related to linear recurrences with constant coefficients

G.f.: x/(1-2*x-x^2).

a(n) = 2*a(n-1)+a(n-2), a(0)=0, a(1)=1.

a(n)=( (1+sqrt(2))^n -(1-sqrt(2))^n )/(2*sqrt(2))

a(n) = integer nearest a(n-1)/(sqrt(2) - 1), where a(0) = 1 - from Clark Kimberling (ck6(AT)evansville.edu)

a(n)= Sum_{i, j, k >= 0: i+j+2k=n} (i+j+k)!/(i!*j!*k!).

a(n)^2 + a(n+1)^2 = a(2n+1) (1999 Putnam examination).

a(2n) = 2*a(n)*A001333(n). - John McNamara, Oct 30, 2002

a(n) = ((-i)^(n-1))*S(n-1, 2*i), with S(n, x) := U(n, x/2) Chebyshev's polynomials of the second kind. See A049310. S(-1, x)=0, S(-2, x)= -1.

Binomial transform of expansion of sinh(sqrt(2)x)/sqrt(2). E.g.f.: exp(x)sinh(sqrt(2)x)/sqrt(2). - Paul Barry (pbarry(AT)wit.ie), May 09 2003

a(n)=sum{k=0, ..floor(n/2), C(n, 2k+1)2^k}. - Paul Barry (pbarry(AT)wit.ie), May 13 2003

a(n-2) + a(n) = (1 + sqrt2)^(n-1) + (1 - sqrt2)^(n-1) = A002203(n-1). [A002203(n)]^2 - 8[a(n)]^2 = 4(-1)^n - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 15 2003

G.f. : x(1+x)/(1-x-3x^2-x^3); a(n)=a(n-1)+3a(n-2)+a(n-2); - Mario Catalani (mario.catalani(AT)unito.it), Jul 23 2004

a(n+1)=Sum(C(n-k, k)2^(n-2k), k=0, .., Floor[n/2]). - Mario Catalani (mario.catalani(AT)unito.it), Jul 23 2004

Apart from initial terms, inverse binomial transform of A052955. - Paul Barry, May 23 2004

a(n)^2+a(n+2k+1)^2=A001653(k)*A001653(n+k);e.g., 5^2+70^2=5*985 - Charlie Marion (charliemath(AT)optonline.net) Aug 03 2005

a(n+1)=sum{k=0..n, binomial((n+k)/2, (n-k)/2)(1+(-1)^(n-k))2^k/2}; - Paul Barry (pbarry(AT)wit.ie), Aug 28 2005

a(n) = a(n - 1) + A001333(n - 1) = A001333(n) - a(n - 1) = A001109(n)/A001333(n) = sqrt(A001110(n)/A001333(n)^2) = ceiling(sqrt(A001108(n)/2)) - Henry Bottomley (se16(AT)btinternet.com), Apr 18 2000

a(n)=F(n, 2), the n-th Fibonacci polynomial evaluated at x=2. - T. D. Noe (noe(AT)sspectra.com), Jan 19 2006

Define c(2n) = -A001108(n), c(2n+1) = -A001108(n+1) and d(2n) = d(2n+1) = A001652(n), then ((-1)^n)*(c(n) + d(n)) = a(n). - Proof given by Max Alekseyev (maxale(AT)gmail.com) - Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Jul 21 2005

a(r+s) = a(r)*a(s+1) + a(r-1)*a(s). - Lekraj Beedassy (blekraj(AT)yahoo.com), Sep 03 2006

a(n)=(b(n+1)+b(n-1))/n where {b(n)} is the sequence A006645 - Sergio Falcon (sfalcon(AT)dma.ulpgc.es), Nov 22 2006

Comments from Miklos Kristof (kristmikl(AT)freemail.hu), Mar 19 2007: (Start)

Let F(n)=a(n)=Pell numbers, L(n)=A002203=companion Pell numbers (A002203):

For a>=b and odd b F(a+b)+F(a-b)=L(a)*F(b).

For a>=b and even b F(a+b)+F(a-b)=F(a)*L(b).

For a>=b and odd b F(a+b)-F(a-b)=F(a)*L(b).

For a>=b and even b F(a+b)-F(a-b)=L(a)*F(b).

F(n+m)+(-1)^m*F(n-m)=F(n)*L(m)

F(n+m)-(-1)^m*F(n-m)=L(n)*F(m)

F(n+m+k)+(-1)^k*F(n+m-k)+(-1)^m*(F(n-m+k)+(-1)^k*F(n-m-k))=F(n)*L(m)*L(k)

F(n+m+k)-(-1)^k*F(n+m-k)+(-1)^m*(F(n-m+k)-(-1)^k*F(n-m-k))=L(n)*L(m)*F(k)

F(n+m+k)+(-1)^k*F(n+m-k)-(-1)^m*(F(n-m+k)+(-1)^k*F(n-m-k))=L(n)*F(m)*L(k)

F(n+m+k)-(-1)^k*F(n+m-k)-(-1)^m*(F(n-m+k)-(-1)^k*F(n-m-k))=8*F(n)*F(m)*F(k) (End)

a(n+1)*a(n)=2*sum{k=0..n, a(k)^2} (a similar relation holds for A001333) - Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Aug 28 2007

a(n+1) = sum(k=0,...,n) binomial(n+1,2k+1) * 2^k = sum(k=0,...,n) A034867(n,k) * 2^k = (1/n!)sum(k=0,...,n) A131980(n,k) * 2^k . - Tom Copeland (tcjpn(AT)msn.com), Nov 30 2007

Equals row sums of unsigned triangle A133156. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 21 2008

a(n) (n>=3) is the determinant of the (n-1) by (n-1) tridiagonal matrix with diagonal entries 2, superdiagonal entries 1 and subdiagonal entries -1. [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 29 2008]

a(n)=5*a(n-2)+2*a(n-3), a(n)=6*a(n-2)-a(n-4). - Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Sep 04 2008

Comments from Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jan 02 2009 (Start): fract((1+sqrt(2))^n)) = (1/2)*(1+(-1)^n)-(-1)^n*(1+sqrt(2))^(-n) = (1/2)*(1+(-1)^n)-(1-sqrt(2))^n.

See A001622 for a general formula concerning the fractional parts of powers of numbers x>1, which suffice x-x^(-1)=floor(x).

a(n) = nint((1+sqrt(2))^n) for n>0. (End)

A000129 := proc(n) option remember; if n <=1 then n; else 2*A000129(n-1)+A000129(n-2); fi; end;

with(numtheory):pel := cfrac (sin(Pi/4), 100): seq(nthnumer(pel, i), i=0..29 ); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 07 2007

A000129:=-1/(-1+2*z+z**2); [S. Plouffe in his 1992 dissertation.]

(Maple) a := n -> (Matrix([[2, 1], [1, 0]])^n)[1, 2]; seq (a(n), n=0..29); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 01 2008]

CoefficientList[Series[x/(1 - 2*x - x^2), {x, 0, 60}], x] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 08 2006

Expand[Table[((1 + Sqrt[2])^n - (1 - Sqrt[2])^n)/(2Sqrt[2]), {n, 0, 30}]] - Artur Jasinski (grafix(AT)csl.pl), Dec 10 2006

a=1; b=0; c=0; lst={b}; Do[c=a+b+c; AppendTo[lst, c]; a=b; b=c, {n, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 23 2009]

(PARI) a(n)=if(n<0, 0, contfracpnqn(vector(n, i, 1+(i>1)))[2, 1])

(Other) sage: [lucas_number1(n, 2, -1) for n in xrange(0, 30)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 22 2009]

(PARI) { default(realprecision, 2000); for (n=0, 4000, a=contfracpnqn(vector(n, i, 1+(i>1)))[2, 1]; if (a > 10^(10^3 - 6), break); write("b000129.txt", n, " ", a); ); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 12 2009]

Partial sums of A001333, also A000129(n)+A000129(n+1) = A001333(n+1).

a(n) = A054456(n-1, 0), n>=1 (first column of triangle).

Cf. A002203, A096669, A096670, A097075, A097076, A051927, A005409.

A077985 is a signed version.

INVERT transform of Fibonacci numbers (A000045).

Cf. A038207.

The following sequences (and others) belong to the same family: A001333, A000129, A026150, A002605, A046717, A015518, A084057, A063727, A002533, A002532, A083098, A083099, A083100, A015519.

Cf. A034867, A131980.

Cf. A133156.

A143808 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 01 2008]

Cf. A135387, A153346. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 29 2008]

Cf. A001622, A006497, A014176, A098316.

A155002 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 18 2009]

A154325 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 12 2009]

Adjacent sequences: A000126 A000127 A000128 this_sequence A000130 A000131 A000132

Sequence in context: A067687 A130009 A048624 this_sequence A141682 A077985 A054198

nonn,easy,core,cofr,nice,frac,new

N. J. A. Sloane (njas(AT)research.att.com).