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 A035646 #16 Aug 16 2020 20:10:41
%S A035646 0,0,0,0,1,0,1,1,1,1,4,1,4,4,4,4,10,4,11,11,11,12,22,12,25,25,26,28,
%T A035646 45,29,52,52,55,60,87,63,101,102,108,118,160,126,187,189,202,221,285,
%U A035646 238,333,338,363,395,492,430,574,585,629,684,828,749,964,987,1061
%N A035646 Number of partitions of n into parts 6k+2 and 6k+3 with at least one part of each type.
%H A035646 Alois P. Heinz, <a href="/A035646/b035646.txt">Table of n, a(n) for n = 1..5000</a> (first 100 terms from Robert Price)
%F A035646 G.f.: (-1 + 1/Product_{k>=0} (1 - x^(6 k + 2)))*(-1 + 1/Product_{k>=0} (1 - x^(6 k + 3))). - _Robert Price_, Aug 16 2020
%t A035646 nmax = 63; s1 = Range[0, nmax/6]*6 + 2; s2 = Range[0, nmax/6]*6 + 3;
%t A035646 Table[Count[IntegerPartitions[n, All, s1~Join~s2],
%t A035646 x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* _Robert Price_, Aug 13 2020 *)
%t A035646 nmax = 63; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(6 k + 2)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(6 k + 3)), {k, 0, nmax}]), {x, 0, nmax}], x] (* _Robert Price_, Aug 16 2020 *)
%Y A035646 Cf. A035441-A035468, A035618-A035645, A035647-A035699.
%K A035646 nonn
%O A035646 1,11
%A A035646 _Olivier Gérard_