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 A294622 #7 Feb 16 2025 08:33:51
%S A294622 1,1,1,1,1,2,2,2,3,3,4,4,4,5,5,6,8,8,9,9,10,13,13,14,16,17,20,20,21,
%T A294622 24,25,28,31,33,36,37,40,45,47,50,55,59,65,67,70,77,81,87,94,99,107,
%U A294622 111,117,127,133,141,152,160,172,178,186,201,210,223,237,249,267,276,289,308,322,341,360,378,401
%N A294622 Number of partitions of n into generalized octagonal numbers (A001082).
%H A294622 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/OctagonalNumber.html">Octagonal Number</a>
%H A294622 <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal numbers</a>
%H A294622 <a href="/index/Par#part">Index entries for related partition-counting sequences</a>
%F A294622 G.f.: Product_{k>=1} 1/((1 - x^(k*(3*k-2)))*(1 - x^(k*(3*k+2)))).
%e A294622 a(8) = 3 because we have [8], [5, 1, 1, 1] and [1, 1, 1, 1, 1, 1, 1, 1].
%t A294622 nmax = 74; CoefficientList[Series[Product[1/((1 - x^(k (3 k - 2))) (1 - x^(k (3 k + 2)))), {k, 1, nmax}], {x, 0, nmax}], x]
%Y A294622 Cf. A001082, A007294, A095699, A279041, A294621, A294624.
%K A294622 nonn
%O A294622 0,6
%A A294622 _Ilya Gutkovskiy_, Nov 05 2017