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 A333815 #14 Jan 17 2025 19:23:30
%S A333815 1,0,0,1,1,0,1,0,0,1,1,1,1,0,0,1,1,0,1,0,1,2,1,0,1,0,0,1,1,1,1,0,0,2,
%T A333815 2,0,1,0,1,1,1,0,1,0,0,2,1,1,1,1,1,1,1,0,1,0,1,2,1,0,1,0,0,1,2,1,1,0,
%U A333815 1,3,1,0,1,0,1,1,1,0,1,1,0,2,1,1,1,0,1,1,1,0,2,1,1,2,2,0,1,0,0,1,1,1,1,0,1
%N A333815 G.f.: Sum_{k>=1} x^(k*(3*k - 1)/2) / (1 - x^(3*k)).
%C A333815 Number of ways to write n as the difference of two pentagonal numbers.
%H A333815 Antti Karttunen, <a href="/A333815/b333815.txt">Table of n, a(n) for n = 1..20000</a>
%F A333815 G.f.: Sum_{i>=0} Sum_{j>=i} Product_{k=i..j} x^(3*k + 1).
%t A333815 nmax = 92; CoefficientList[Series[Sum[x^(k (3 k - 1)/2)/(1 - x^(3 k)), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%o A333815 (PARI) A333815list(up_to_n) = { my(s=Ser(sum(k=1,up_to_n,'x^(k*(3*k - 1)/2) / (1 - 'x^(3*k))), 'x, 1+up_to_n)); vector(up_to_n,i,polcoeff(s,i)); }; \\ - _Antti Karttunen_, Jan 17 2025
%o A333815 (PARI)
%o A333815 A000326(n) = (n*(3*n-1)/2);
%o A333815 A333815(n) = { my(u=1+floor((n-1)/3), s=0); forstep(i=u,0,-1,my(p2=A000326(i)); if(p2<n, return(s)); s += ispolygonal(p2-n, 5)); (s); }; \\ _Antti Karttunen_, Jan 17 2025
%Y A333815 Cf. A000326, A001227, A034178, A255849, A333816, A333817, A333818.
%K A333815 nonn
%O A333815 1,22
%A A333815 _Ilya Gutkovskiy_, Apr 06 2020
%E A333815 Data section extended up to a(105) by _Antti Karttunen_, Jan 17 2025