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 A035621 #15 Aug 16 2020 16:32:14
%S A035621 0,0,0,0,1,1,1,1,4,4,4,4,10,11,11,11,22,25,26,26,44,51,54,55,84,98,
%T A035621 105,108,153,178,193,200,269,313,341,356,459,531,582,611,764,880,967,
%U A035621 1021,1244,1424,1568,1662,1988,2264,2494,2653,3122,3536,3896,4155
%N A035621 Number of partitions of n into parts 4k and 4k+1 with at least one part of each type.
%H A035621 Alois P. Heinz, <a href="/A035621/b035621.txt">Table of n, a(n) for n = 1..1000</a> (first 100 terms from Robert Price)
%F A035621 G.f.: (-1 + 1/Product_{k>=1} (1 - x^(4 k)))*(-1 + 1/Product_{k>=0} (1 - x^(4 k + 1))). - _Robert Price_, Aug 16 2020
%t A035621 nmax = 56; s1 = Range[1, nmax/4]*4; s2 = Range[0, nmax/4]*4 + 1;
%t A035621 Table[Count[IntegerPartitions[n, All, s1~Join~s2],
%t A035621 x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* _Robert Price_, Aug 06 2020 *)
%t A035621 nmax = 56; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(4 k)), {k, 1, nmax}])*(-1 + 1/Product[(1 - x^(4 k + 1)), {k, 0, nmax}]), {x, 0, nmax}], x] (* _Robert Price_, Aug 16 2020*)
%Y A035621 Cf. A035441-A035468, A035618-A035620, A035622-A035699.
%K A035621 nonn
%O A035621 1,9
%A A035621 _Olivier Gérard_