0,2

Comment from Hans Isdahl (hansi(AT)nordtroms.net), Jan 26 2008: The brown rat (rattus norwegicus) breeds very quickly. It can give birth to other rats 7 times a year, starting at the age of three months. The average number of pups is 8. The present sequence gives the total number of rats, when the intervals are 12/7 of a year and a young rat starts having offspring at 24/7 of a year.

Numbers n such that tau(n) is odd where tau(x) denotes the Ramanujan tau function (A000594). - Benoit Cloitre (benoit7848c(AT)orange.fr), May 01 2003

If Y is a fixed 2-subset of a (2n+1)-set X then a(n-1) is the number of 3-subsets of X intersecting Y. - Milan R. Janjic (agnus(AT)blic.net), Oct 21 2007

All terms of this sequence are of the form 8k+1. For numbers 8k+1 which aren't squares see A138393. Numbers 8k+1 are squares iff k is a triangular number from A000217. And squares have form 4n(n+1)+1. - Artur Jasinski (grafix(AT)csl.pl), Mar 27 2008

Sequence arises from reading the line from 1, in the direction 1, 25,... and the line from 9, in the direction 9, 49,..., in the square spiral whose vertices are the squares A000290. - Omar E. Pol (info(AT)polprimos.com), May 24 2008

First quadrisection of A061038: A061038(4n). From Balmer spectrum of hydrogen. [From Paul Curtz (bpcrtz(AT)free.fr), Oct 26 2008]

Sum_{n>=0} 1/a(n) = Pi^2/8 [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Mar 07 2009]

Equals the triangular numbers convolved with [1, 6, 1, 0, 0, 0,...] [From Gary W. Adamson & Alexander Povolotsky (qntmpkt(AT)yahoo.com), May 29 2009]

Except for the first term, a(n)=8*n+a(n-1), (with a(1)=9) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Oct 24 2009]

First differences: A008590(n) = a(n) - a(n-1) for n>0. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 08 2009]

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

Index entries for sequences related to linear recurrences with constant coefficients

Milan Janjic, Two Enumerative Functions

B. C. Berndt & K. Ono, Ramanujan's unpublished manuscript on the partition and tau functions with proofs and commentary

Eric Weisstein's World of Mathematics, Moore Neighborhood

Index entries for sequences related to centered polygonal numbers

a(n) = 1 + Sum [(8*i),{i,1,n}] =(2n+1)^2 - Zak Seidov, May 07 2006

Binomial transform of [1, 8, 8, 0, 0, 0,...]; Narayana transform (A001263) of [1, 8, 0, 0, 0,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 29 2007

O.g.f.: (1+6*x+x^2)/(1-x)^3 = 1/(1-x)-8/(1-x)^2+8/(1-x)^3 . - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 11 2008

a(n) = 8n(n + 1))/2 + 1 = 4n (n + 1) + 1 = 4n^2 + 4n + 1 - Artur Jasinski (grafix(AT)csl.pl), Mar 27 2008

a(n) = A000290(A005408(n)). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 08 2009]

a(n)=8*n+a(n-1)-8 (with a(1)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 09 2009]

For n=2, a(2)=8*2+1-8=9; n=3, a(3(=8*3+9-8=25; n=4, a(4)=8*4+25-8=49 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 09 2009]

a = {}; Do[If[Sqrt[8k + 1] == Floor[Sqrt[8k + 1]], AppendTo[a, 8k + 1]], {k, 0, 1000}]; a or Table[4n(n + 1) + 1, {n, 0, 500}] - Artur Jasinski (grafix(AT)csl.pl), Mar 27 2008

(Other) sage: [crt(2, n, 4, 5)^2/2^2 for n in xrange(3, 47)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 07 2009]

Cf. A016742, A033996.

Cf. A001263.

Cf. A000217, A138393.

Cf. A000290, A001539, A016742, A016802, A016814, A016826, A016838.

a(n) = A033951(n) + n. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 17 2009]

Cf. A167661, A167700. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 09 2009]

Sequence in context: A075026 A113659 A113745 this_sequence A110487 A030156 A141768

Adjacent sequences: A016751 A016752 A016753 this_sequence A016755 A016756 A016757

nonn,easy,new

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

Additional description from Terry Trotter, Apr 06 2002.

More terms from Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 30 2006