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 A216222 #25 Jun 12 2025 15:52:57
%S A216222 1,1,2,1,1,2,3,4,3,3,3,3,6,7,8,10,9,9,9,9,11,13,16,20,22,25,28,27,28,
%T A216222 29,30,32,35,40,45,53,60,67,73,79,85,87,92,95,98,105,111,120,132,145,
%U A216222 160,178,196,212,231,247,263,280,291,305,319,334,352,371,393
%N A216222 Counting a set of restricted partitions.
%H A216222 Vaclav Kotesovec, <a href="/A216222/b216222.txt">Table of n, a(n) for n = 0..10000</a>
%F A216222 G.f.: Sum_{k>=0} x^(k^2) * Product_{j=1..k} (1 + x^j)^2 = 1 +x^1*(1+x)^2 +x^4*(1+x)^2*(1+x^2)^2 +...+ x^k^2*(1+x)^2*(1+x^2)^2*(1+x^3)^2*...*(1+x^k)^2+...
%F A216222 a(n) ~ phi^(3/2) * exp(Pi*sqrt(2*n/15)) / (4*5^(1/4)*sqrt(n)), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - _Vaclav Kotesovec_, Sep 29 2024
%t A216222 Take[CoefficientList[Sum[x^(k^2)*Product[1 + x^i, {i, k}]^2, {k, 0, 7}], x], 63] (* _Giovanni Resta_, Mar 13 2013 *)
%t A216222 nmax = 100; p = 1; s = 1; Do[p = Expand[p*(1 + x^k)*(1 + x^k)*x^(2*k - 1)]; p = Take[p, Min[nmax + 1, Exponent[p, x] + 1, Length[p]]]; s += p; , {k, 1, Sqrt[nmax]}]; Take[CoefficientList[s, x], nmax + 1] (* _Vaclav Kotesovec_, Oct 09 2024 *)
%Y A216222 Cf. A001622, A306734, A376542, A376580, A376812, A376813.
%K A216222 nonn
%O A216222 0,3
%A A216222 _David S. Newman_, Mar 13 2013
%E A216222 a(14)-a(62) from _Giovanni Resta_, Mar 13 2013