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 A035624 #15 Aug 16 2020 16:33:36
%S A035624 0,0,1,1,2,2,5,5,8,8,14,15,22,23,34,37,51,54,74,81,107,116,150,165,
%T A035624 210,229,287,316,392,430,526,580,704,774,929,1024,1223,1347,1593,1756,
%U A035624 2068,2278,2663,2933,3416,3762,4355,4793,5529,6084,6985,7680,8789
%N A035624 Number of partitions of n into parts 4k+1 and 4k+2 with at least one part of each type.
%H A035624 Alois P. Heinz, <a href="/A035624/b035624.txt">Table of n, a(n) for n = 1..1000</a> (first 100 terms from Robert Price)
%F A035624 G.f.: (-1 + 1/Product_{k>=0} (1 - x^(4 k + 1)))*(-1 + 1/Product_{k>=0} (1 - x^(4 k + 2))). - _Robert Price_, Aug 16 2020
%t A035624 nmax = 53; s1 = Range[0, nmax/4]*4 + 1; s2 = Range[0, nmax/4]*4 + 2;
%t A035624 Table[Count[IntegerPartitions[n, All, s1~Join~s2],
%t A035624 x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* _Robert Price_, Aug 06 2020 *)
%t A035624 nmax = 53; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(4 k + 2)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(4 k + 1)), {k, 0, nmax}]), {x, 0, nmax}], x] (* _Robert Price_, Aug 16 2020 *)
%Y A035624 Cf. A035441-A035468, A035618-A035623, A035625-A035699.
%K A035624 nonn
%O A035624 1,5
%A A035624 _Olivier Gérard_