0,2

Number of ordered trees with n edges and height at most 4.

Number of palindromic structures using a maximum of three different symbols. - Marks R. Nester (nesterm(AT)dpi.qld.gov.au)

Consider the mapping f(a/b) = (a + 2b)/(2a + b). Taking a = 1 b = 2 to start with and carrying out this mapping repeatedly on each new (reduced) rational number gives the following sequence 1/2,4/5,13/14,40/41,... converging to 1. Sequence contains the denominators = (3^n+1)/2. The same mapping for N i.e. f(a/b) = (a + Nb)/(a+b) gives fractions converging to N^(1/2). - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Mar 22 2003

Second binomial transform of expansion of cosh(x). - Paul Barry (pbarry(AT)wit.ie), Apr 05 2003

The sequence (1,1,2,5,..)=3^n/6+1/2+0^n/3 has binomial transform A007581. - Paul Barry (pbarry(AT)wit.ie), Jul 20 2003

Number of (s(0), s(1), ..., s(2n+2)) such that 0 < s(i) < 6 and |s(i) - s(i-1)| = 1 for i = 1,2,....,2n+2, s(0) = 1, s(2n+2) = 1. - Herbert Kociemba (kociemba(AT)t-online.de), Jun 10 2004

Density of regular language L over {1,2,3}^* (i.e. number of strings of length n in L) described by regular expression 11*+11*2(1+2)*+11*2(1+2)*3(1+2+3)*. - Nelma Moreira (nam(AT)ncc.up.pt), Oct 10 2004

Sums of rows of the triangle in A119258. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 11 2006

Number of n-words from the alphabet A={a,b,c} which contain an even number of a's. - Fung Cheok Yin (cheokyin_restart(AT)yahoo.com.hk), Aug 30 2006

Let P(A) be the power set of an n-element set A. Then a(n) = the number of pairs of elements {x,y} of P(A) for which either 0) x and y are disjoint and for which x is not a subset of y and y is not a subset of x, or 1) x = y. - Ross La Haye (rlahaye(AT)new.rr.com), Jan 10 2008

a(n+1) gives the number of primitive periodic multiplex juggling sequences of length n with base state <2>. - Steve Butler (sbutler(AT)math.ucsd.edu), Jan 21 2008

a(n) is also the number of idempotent order-preserving and order-decreasing partial transformations (of an n-chain). [From A. Umar (aumarh(AT)squ.edu.om), Oct 02 2008]

Equals row sums of triangle A147292 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 05 2008]

Equals leftmost column of A071919^3 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 13 2009]

Contribution from Parthasarathy Nambi (PachaNambi(AT)yahoo.com), Jun 03 2009: (Start)

Repetitive digit sum of terms in the sequence gives 5. Here are few examples:

47071589414 is a term in this sequence, whose repetitive digit sum is: 47071589414 --> 50 --> 5

141214768241 is a term in this sequence, whose repetitive digit sum is: 141214768241 --> 41 --> 5

423644304722 is a term in this sequence, whose repetitive digit sum is: 423644304722 --> 41 --> 5

(End)

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Hwang, F. K. and Mallows, C. L.; Enumerating nested and consecutive partitions. J. Combin. Theory Ser. A 70 (1995), no. 2, 323-333.

M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia.

P. Ribenboim, The Book of Prime Number Records. Springer-Verlag, NY, 2nd ed., 1989, p. 60.

P. Ribenboim, The Little Book of Big Primes, Springer-Verlag, NY, 1991, p. 53.

Nelma Moreira and Rogerio Reis, On the density of languages representing finite set partitions, Technical Report DCC-2004-07, August 2004, DCC-FC& LIACC, Universidade do Porto.

Kin Y. Li, Mathematical Excalibur, 4(1999) Number 4, p. 3, Problem 83

N. Moreira and R. Reis, On the Density of Languages Representing Finite Set Partitions, Journal of Integer Sequences, Vol. 8 (2005), Article 05.2.8.

S. Butler and R. Graham, Enumerating (multiplex) juggling sequences, arXiv:0801.2597

Encyclopedia of Combinatorial Structures, Entry 454, divided by 2.

Laradji, A. and Umar, A. Combinatorial results for semigroups of order-decreasing partial transformations J. Integer Seq. 7 (2004), 04.3.8, 14 pp. [From A. Umar (aumarh(AT)squ.edu.om), Oct 02 2008]

Ross La Haye, Binary Relations on the Power Set of an n-Element Set, Journal of Integer Sequences, Vol. 12 (2009), Article 09.2.6. [From Ross La Haye (rlahaye(AT)new.rr.com), Feb 22 2009]

T. D. Noe, Table of n, a(n) for n=0..200

Index entries for sequences related to linear recurrences with constant coefficients

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

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 163

Nelma Moreira and Rogerio Reis, dcc-2004-07.ps

Eric Weisstein's World of Mathematics, Mephisto Waltz Sequence

Kin Y. Li, Problem 83

Laradji, A. and Umar, A., Combinatorial Results for Semigroups of Order-Decreasing Partial Transformations , Journal of Integer Sequences, Vol. 7 (2004), Article 04.3.8. [From A. Umar (aumarh(AT)squ.edu.om), Oct 02 2008]

a(n)=3*a(n-1)-1.

Binomial transform of Chebyshev coefficients A011782. - Paul Barry (pbarry(AT)wit.ie), Mar 16 2003

a(n)=4a(n-1)-3a(n-2), a(0)=1, a(1)=2. G.f.: (1-2x)/((1-x)(1-3x)). - Paul Barry (pbarry(AT)wit.ie), Mar 16 2003

E.g.f. exp(2x)cosh(x) - Paul Barry (pbarry(AT)wit.ie), Apr 05 2003

a(n)=sum{k=0..floor(n/2); C(n, 2k)2^(n-2k) } - Paul Barry (pbarry(AT)wit.ie), May 08 2003

This sequence is also the partial sums of the first 3 Stirling numbers of second kind: a(n) = S(n+1, 1)+S(n+1, 2)+S(n+1, 3) for n>=0; alternatively it is the number of partitions of [n+1] into 3 or fewer parts. - Mike Zabrocki (zabrocki(AT)mathstat.yorku.ca), Jun 21 2004

For c=3, a(n)= (c^n)/c!+sum_{k=1..c-2}((k^n)/k!*(sum_{j=2..c-k}(((-1)^j)/j!))) or = sum_{k=1..c}(g(k, c)*k^n) where g(1, 1)=1 g(1, c)=g(1, c-1)+((-1)^(c-1))/(c-1)!, c>1 g(k, c)=g(k-1, c-1)/k, for c>1 and 2<= k<= c - Nelma Moreira (nam(AT)ncc.up.pt), Oct 10 2004

The i-th term of the sequence is the entry (1, 1) in the i-th power of the 2 by 2 matrix M=((2, 1), (1, 2)). - Simone Severini (ss54(AT)york.ac.uk), Oct 15 2005

with (combinat):seq(sum(stirling2(n, j), j=1..3), n=1..26); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 04 2007

ZL := [S, {S=Union(Sequence(Z), Sequence(Union(Z, Z, Z)))}, unlabeled]: seq(combstruct[count](ZL, size=n)/2, n=0..25); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 19 2008

Table[(3^n + 1)/2, {n, 0, 50}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 08 2006

a=1; lst={a}; Do[a=a*3-1; AppendTo[lst, a], {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 25 2008]

sage: [lucas_number2(n, 4, 3)/2 for n in xrange(0, 33)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 08 2008

(Other) sage: [(sigma(3, n-1))/2 for n in xrange(1, 27)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 05 2009]

Cf. A056449, A064881-A064886.

Cf. A008277.

Cf. A007581, A056272, A056273.

Cf. A000392, A000079.

Cf. A034472.

A147292 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 05 2008]

Cf. A003462 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 25 2008]

A071919 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 13 2009]

Sequence in context: A122055 A116845 A116849 this_sequence A124302 A123183 A088355

Adjacent sequences: A007048 A007049 A007050 this_sequence A007052 A007053 A007054

easy,nonn,nice

Colin Mallows, N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe, Robert G. Wilson v (rgwv(AT)rgwv.com)