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 A035636 #15 Aug 16 2020 18:36:34
%S A035636 0,0,0,0,0,0,1,0,0,1,1,2,1,1,3,3,4,3,4,7,7,8,8,10,14,14,16,18,20,27,
%T A035636 28,30,35,40,48,52,55,64,73,85,90,98,114,128,143,155,168,195,214,237,
%U A035636 259,283,319,353,385,422,460,516,564,618,672,734,816,892,964,1057
%N A035636 Number of partitions of n into parts 5k+3 and 5k+4 with at least one part of each type.
%H A035636 Robert Price, <a href="/A035636/b035636.txt">Table of n, a(n) for n = 1..1000</a>
%F A035636 G.f.: (-1 + 1/Product_{k>=0} (1 - x^(5 k + 3)))*(-1 + 1/Product_{k>=0} (1 - x^(5 k + 4))). - _Robert Price_, Aug 16 2020
%t A035636 nmax = 66; s1 = Range[0, nmax/5]*5 + 3; s2 = Range[0, nmax/5]*5 + 4;
%t A035636 Table[Count[IntegerPartitions[n, All, s1~Join~s2],
%t A035636 x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* _Robert Price_, Aug 07 2020 *)
%t A035636 nmax = 66; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(5 k + 3)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(5 k + 4)), {k, 0, nmax}]), {x, 0, nmax}], x] (* _Robert Price_, Aug 16 2020 *)
%Y A035636 Cf. A035441-A035468, A035618-A035635, A035637-A035699.
%K A035636 nonn
%O A035636 1,12
%A A035636 _Olivier Gérard_