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 A035663 #15 Aug 16 2020 21:18:51
%S A035663 0,0,0,0,0,1,0,1,0,2,0,2,2,3,2,3,4,4,4,7,6,9,6,13,8,15,12,19,16,21,23,
%T A035663 25,27,32,35,40,39,53,47,63,57,78,71,88,91,104,109,121,135,146,154,
%U A035663 179,182,213,209,257,250,295,300,344,356,392,426,459,491,539,572,633
%N A035663 Number of partitions of n into parts 7k+2 and 7k+4 with at least one part of each type.
%H A035663 Alois P. Heinz, <a href="/A035663/b035663.txt">Table of n, a(n) for n = 1..1000</a> (first 125 terms from Robert Price)
%F A035663 G.f.: (-1 + 1/Product_{k>=0} (1 - x^(7 k + 2)))*(-1 + 1/Product_{k>=0} (1 - x^(7 k + 4))). - _Robert Price_, Aug 16 2020
%t A035663 nmax = 68; s1 = Range[0, nmax/7]*7 + 2; s2 = Range[0, nmax/7]*7 + 4;
%t A035663 Table[Count[IntegerPartitions[n, All, s1~Join~s2],
%t A035663 x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* _Robert Price_, Aug 14 2020 *)
%t A035663 nmax = 68; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(7 k + 2)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(7 k + 4)), {k, 0, nmax}]), {x, 0, nmax}], x] (* _Robert Price_, Aug 16 2020 *)
%Y A035663 Cf. A035441-A035468, A035618-A035662, A035664-A035699.
%K A035663 nonn
%O A035663 1,10
%A A035663 _Olivier Gérard_