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 A035643 #14 Aug 16 2020 19:16:42
%S A035643 0,0,0,1,1,1,2,2,2,5,5,5,8,8,8,14,15,15,22,23,23,34,37,38,51,54,55,74,
%T A035643 81,84,108,116,119,151,165,172,213,230,238,290,317,332,399,433,451,
%U A035643 535,583,613,720,781,818,950,1033,1088,1257,1363,1432,1638,1777,1875
%N A035643 Number of partitions of n into parts 6k+1 and 6k+3 with at least one part of each type.
%H A035643 Robert Price, <a href="/A035643/b035643.txt">Table of n, a(n) for n = 1..1000</a>
%F A035643 G.f.: (-1 + 1/Product_{k>=0} (1 - x^(6 k + 1)))*(-1 + 1/Product_{k>=0} (1 - x^(6 k + 3))). - _Robert Price_, Aug 16 2020
%t A035643 nmax = 60; s1 = Range[0, nmax/6]*6 + 1; s2 = Range[0, nmax/6]*6 + 3;
%t A035643 Table[Count[IntegerPartitions[n, All, s1~Join~s2],
%t A035643 x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* _Robert Price_, Aug 13 2020 *)
%t A035643 nmax = 60; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(6 k + 1)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(6 k + 3)), {k, 0, nmax}]), {x, 0, nmax}], x] (* _Robert Price_, Aug 16 2020 *)
%Y A035643 Cf. A035441-A035468, A035618-A035642, A035644-A035699.
%K A035643 nonn
%O A035643 1,7
%A A035643 _Olivier Gérard_