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 A035685 #10 Aug 16 2020 14:08:18
%S A035685 0,0,0,0,1,0,1,1,1,1,2,1,4,2,4,4,5,4,7,5,10,7,12,11,14,13,18,15,24,19,
%T A035685 28,27,33,31,42,36,51,45,60,58,71,68,87,79,103,96,120,118,141,137,169,
%U A035685 159,197,189,228,226,266,262,314,302,362,355,416,416,482,478,561,550
%N A035685 Number of partitions of n into parts 8k+2 and 8k+3 with at least one part of each type.
%H A035685 Robert Price, <a href="/A035685/b035685.txt">Table of n, a(n) for n = 1..1000</a>
%F A035685 G.f.: (-1 + 1/Product_{k>=0} (1 - x^(8 k + 2)))*(-1 + 1/Product_{k>=0} (1 - x^(8 k + 3))). - _Robert Price_, Aug 15 2020
%t A035685 nmax = 68; s1 = Range[0, nmax/8]*8 + 2; s2 = Range[0, nmax/8]*8 + 3;
%t A035685 Table[Count[IntegerPartitions[n, All, s1~Join~s2],
%t A035685 x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* _Robert Price_, Aug 15 2020 *)
%t A035685 nmax = 68; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(8 k + 2)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(8 k + 3)), {k, 0, nmax}]), {x, 0, nmax}], x] (* _Robert Price_, Aug 15 2020*)
%Y A035685 Cf. A035441-A035468, A035618-A035684, A035686-A035699.
%K A035685 nonn
%O A035685 1,11
%A A035685 _Olivier Gérard_