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

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

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B. C. Berndt & K. Ono, Ramanujan's unpublished manuscript on the partition and tau functions with proofs and commentary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

Cf. A016742, A033996.

Cf. A001263.

Cf. A000217, A138393.

Adjacent sequences: A016751 A016752 A016753 this_sequence A016755 A016756 A016757

Sequence in context: A075026 A113659 A113745 this_sequence A110487 A030156 A110284

nonn,easy

njas

Additional description from Terry Trotter, Apr 06 2002.

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