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 A035631 #17 Aug 16 2020 17:13:33
%S A035631 0,0,1,1,2,2,3,5,6,8,9,11,15,18,23,26,31,38,45,55,62,73,85,100,118,
%T A035631 135,155,178,205,238,269,308,347,397,452,512,578,650,733,829,929,1045,
%U A035631 1164,1307,1461,1635,1822,2026,2254,2511,2787,3098,3422,3796,4196
%N A035631 Number of partitions of n into parts 5k+1 and 5k+2 with at least one part of each type.
%H A035631 Robert Price, <a href="/A035631/b035631.txt">Table of n, a(n) for n = 1..1000</a>
%F A035631 G.f.: (-1 + 1/Product_{k>=0} (1 - x^(5 k + 1)))*(-1 + 1/Product_{k>=0} (1 - x^(5 k + 2))). - _Robert Price_, Aug 16 2020
%t A035631 nmax = 55; s1 = Range[0, nmax/5]*5 + 1; s2 = Range[0, nmax/5]*5 + 2;
%t A035631 Table[Count[IntegerPartitions[n, All, s1~Join~s2],
%t A035631 x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* _Robert Price_, Aug 06 2020 *)
%t A035631 nmax = 55; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(5 k + 1)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(5 k + 2)), {k, 0, nmax}]), {x, 0, nmax}], x] (* _Robert Price_, Aug 16 2020 *)
%Y A035631 Cf. A035371.
%Y A035631 Cf. A035441-A035468, A035618-A035630, A035632-A035699.
%K A035631 nonn
%O A035631 1,5
%A A035631 _Olivier Gérard_