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 A035686 #10 Aug 16 2020 14:08:26
%S A035686 0,0,0,0,0,1,0,1,0,2,0,2,0,5,0,5,0,8,0,8,0,14,0,15,0,22,0,23,0,34,0,
%T A035686 37,0,51,0,54,0,74,0,81,0,107,0,116,0,150,0,165,0,210,0,229,0,287,0,
%U A035686 316,0,392,0,430,0,526,0,580,0,704,0,774,0,929,0,1024,0,1223,0,1347,0
%N A035686 Number of partitions of n into parts 8k+2 and 8k+4 with at least one part of each type.
%H A035686 Robert Price, <a href="/A035686/b035686.txt">Table of n, a(n) for n = 1..1000</a>
%F A035686 G.f.: (-1 + 1/Product_{k>=0} (1 - x^(8 k + 2)))*(-1 + 1/Product_{k>=0} (1 - x^(8 k + 4))). - _Robert Price_, Aug 15 2020
%t A035686 nmax = 77; s1 = Range[0, nmax/8]*8 + 2; s2 = Range[0, nmax/8]*8 + 4;
%t A035686 Table[Count[IntegerPartitions[n, All, s1~Join~s2],
%t A035686 x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* _Robert Price_, Aug 15 2020 *)
%t A035686 nmax = 77; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(8 k + 2)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(8 k + 4)), {k, 0, nmax}]), {x, 0, nmax}], x] (* _Robert Price_, Aug 15 2020*)
%Y A035686 Cf. A035441-A035468, A035618-A035685, A035687-A035699.
%K A035686 nonn
%O A035686 1,10
%A A035686 _Olivier Gérard_