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 A363075 #17 Jun 20 2025 02:35:37
%S A363075 0,0,0,0,1,1,2,3,6,6,10,12,18,20,27,32,42,47,59,67,85,94,113,126,152,
%T A363075 169,198,220,257,282,326,359,413,452,512,563,639,695,781,853,958,1041,
%U A363075 1161,1261,1402,1524,1685,1827,2021,2186,2407,2604,2861,3088,3385,3657,4002,4316,4704,5069,5531
%N A363075 Number of partitions of n such that 3*(least part) + 1 = greatest part.
%H A363075 Vaclav Kotesovec, <a href="/A363075/b363075.txt">Table of n, a(n) for n = 1..5000</a>
%F A363075 G.f.: Sum_{k>=1} x^(4*k+1)/Product_{j=k..3*k+1} (1-x^j).
%F A363075 a(n) ~ c * A376815^sqrt(n) / sqrt(n), where c = 0.33761... - _Vaclav Kotesovec_, Jun 20 2025
%t A363075 nmax = 100; p = 1; s = 0; Do[p = Simplify[p*(1 - x^(3*k - 2))*(1 - x^(3*k - 1))*(1 - x^(3*k))/(1 - x^k)]; p = Normal[p + O[x]^(nmax + 1)]; s += x^(4*k + 1)/(1 - x^k)/(1 - x^(3*k + 1))/p;, {k, 1, nmax}]; Rest[CoefficientList[Series[s, {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Jun 19 2025 *)
%o A363075 (PARI) my(N=70, x='x+O('x^N)); concat([0, 0, 0, 0], Vec(sum(k=1, N, x^(4*k+1)/prod(j=k, 3*k+1, 1-x^j))))
%Y A363075 Cf. A049820, A237828, A363076, A363077.
%Y A363075 Cf. A237825.
%K A363075 nonn
%O A363075 1,7
%A A363075 _Seiichi Manyama_, May 17 2023