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 A035644 #14 Aug 16 2020 20:09:47
%S A035644 0,0,0,0,1,1,1,1,2,2,4,4,5,5,7,7,11,12,14,14,19,20,26,28,34,35,43,45,
%T A035644 56,61,72,75,90,96,113,122,143,151,175,186,216,233,268,284,325,348,
%U A035644 395,424,483,515,580,619,697,748,841,897,1002,1072,1193,1277,1425
%N A035644 Number of partitions of n into parts 6k+1 and 6k+4 with at least one part of each type.
%H A035644 Robert Price, <a href="/A035644/b035644.txt">Table of n, a(n) for n = 1..1000</a>
%F A035644 G.f.: (-1 + 1/Product_{k>=0} (1 - x^(6 k + 1)))*(-1 + 1/Product_{k>=0} (1 - x^(6 k + 4))). - _Robert Price_, Aug 16 2020
%t A035644 nmax = 61; s1 = Range[0, nmax/6]*6 + 1; s2 = Range[0, nmax/6]*6 + 4;
%t A035644 Table[Count[IntegerPartitions[n, All, s1~Join~s2],
%t A035644 x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* _Robert Price_, Aug 13 2020 *)
%t A035644 nmax = 61; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(6 k + 1)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(6 k + 4)), {k, 0, nmax}]), {x, 0, nmax}], x] (* _Robert Price_, Aug 16 2020 *)
%Y A035644 Cf. A035441-A035468, A035618-A035643, A035645-A035699.
%K A035644 nonn
%O A035644 1,9
%A A035644 _Olivier Gérard_