This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A279041 #11 Feb 16 2025 08:33:37
%S A279041 1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,4,4,4,5,5,5,5,5,6,6,6,7,7,
%T A279041 7,7,7,8,8,8,10,10,11,11,11,12,12,12,14,14,15,15,15,16,16,16,18,18,19,
%U A279041 19,19,21,21,22,24,25,26,26,26,28,28,29,31,32,33,33,33,35,35,36,39,40,42,42,43,45,46,47,50,51,53
%N A279041 Expansion of Product_{k>=1} 1/(1 - x^(k*(3*k-2))).
%C A279041 Number of partitions of n into nonzero octagonal numbers (A000567).
%H A279041 Alois P. Heinz, <a href="/A279041/b279041.txt">Table of n, a(n) for n = 0..20000</a>
%H A279041 M. Bernstein and N. J. A. Sloane, <a href="http://arXiv.org/abs/math.CO/0205301">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]
%H A279041 M. Bernstein and N. J. A. Sloane, <a href="/A003633/a003633_1.pdf">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
%H A279041 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/OctagonalNumber.html">Octagonal Number</a>
%H A279041 <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal numbers</a>
%H A279041 <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>
%F A279041 G.f.: Product_{k>=1} 1/(1 - x^(k*(3*k-2))).
%e A279041 a(9) = 2 because we have [8, 1] and [1, 1, 1, 1, 1, 1, 1, 1, 1].
%p A279041 h:= proc(n) option remember; `if`(n<1, 0, (t->
%p A279041 `if`(t*(3*t-2)>n, t-1, t))(1+h(n-1)))
%p A279041 end:
%p A279041 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A279041 b(n, i-1)+(t-> b(n-t, min(i, h(n-t))))(i*(3*i-2))))
%p A279041 end:
%p A279041 a:= n-> b(n, h(n)):
%p A279041 seq(a(n), n=0..100); # _Alois P. Heinz_, Dec 28 2018
%t A279041 nmax=90; CoefficientList[Series[Product[1/(1 - x^(k (3 k - 2))), {k, 1, nmax}], {x, 0, nmax}], x]
%Y A279041 Cf. A000567, A001156, A007294, A037444, A218379, A278949, A279012.
%K A279041 nonn,easy
%O A279041 0,9
%A A279041 _Ilya Gutkovskiy_, Dec 04 2016