0,3

Binomial transform of (0,1,5,0,0,0,...) Binomial transform is A084899. - Paul Barry (pbarry(AT)wit.ie), Jun 10 2003

Also the partial sums of A016861, a zero added in front; therefore a(n) = n (mod 5). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 19 2008

a(n+1) = A153126(n) + n mod 2; a(2*n+1)=A033571(n); a(2*(n+1))=A153127(n)+1. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Dec 20 2008]

Also, let Hep(n) = heptagonal numbers, T(n)= triangular numbers, then Hep(n)= T(n)+4*T(n-1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Jan 28 2009]

Comment from Ken Rosenbaum, Dec 02 2009: if you multiply the terms of this sequence by 40 and add 9, you get A017354, which is the list of squares of all whole numbers ending in 7 (this is easy to prove).

A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 189.

L. E. Dickson, History of the Theory of Numbers. Carnegie Institute Public. 256, Washington, DC, Vol. 1, 1919; Vol. 2, 1920; Vol. 3, 1923, see vol. 2, p. 2.

B. S. Rao, Heptagonal numbers in the Pell sequence and Diophantine equations 2x^2 = y^2(5y-3)^2 +- 2, Fib. Quarterly, 43 (2005), 194-201.

B. S. Rao, Heptagonal numbers in the associated Pell sequence ..., Fib. Quarterly, 43 (2005), 302-306.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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

T. D. Noe, Table of n, a(n) for n=0..1000

Index entries for sequences related to linear recurrences with constant coefficients

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 341

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.

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

G.f.: x(1+4x)/(1-x)^3; a(n)=C(n, 1)+5C(n, 2). - Paul Barry (pbarry(AT)wit.ie), Jun 10 2003

a(n)=sum{k=1..n, 4n-3k}. - Paul Barry (pbarry(AT)wit.ie), Sep 06 2005

a(n)=n+5*A000217(n-1) - Floor van Lamoen (fvlamoen(AT)hotmail.com), Oct 14 2005

Row sums of triangle A131413 - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 08 2007

Sequence starting (1, 7, 18, 34,...) = binomial transform of (1, 6, 5, 0, 0, 0,...). Also row sums of triangle A131896. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 24 2007

a(n)=3a(n-1)-3a(n-2)+a(n-3), a(0)=0, a(1)=1, a(2)=7 [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Dec 02 2008]

a(n)=5*n+a(n-1)-9 (with a(1)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 12 2009]

For n=2, a(2)=5*2+0-9=1; n=3, a(3)=5*3+1-9=7; n=4, a(4)=5*4+7-9=18 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 12 2009]

A000566:=-(1+4*z)/(z-1)**3; [S. Plouffe in his 1992 dissertation.]

a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=2*a[n-1]-a[n-2]+5 od: seq(a[n], n=0..48); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 18 2008

s=0; lst={s}; Do[s+=n+1; AppendTo[lst, s], {n, 0, 6!, 5}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 25 2008]

Cf. A014637, A014640, A014773, A014792, A069099.

a(n)= A093562(n+1, 2), (5, 1)-Pascal column.

Cf. A131413.

Cf. A131896.

Cf. A134483.

Cf. A000217, A000384, A000567.

Sequence in context: A049532 A156619 A033537 this_sequence A133673 A023166 A002764

Adjacent sequences: A000563 A000564 A000565 this_sequence A000567 A000568 A000569

nonn,easy,nice,new

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