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 A036801 #12 Oct 10 2024 15:14:11
%S A036801 1,1,2,3,5,6,10,13,19,25,34,44,60,76,100,128,165,207,265,330,420,519,
%T A036801 649,799,993,1224,1502,1834,2244,2724,3332,4016,4865,5856,7058,8490,
%U A036801 10171,12154,14523,17296,20639,24460,29031,34340,40616,47987,56520,66489,78159
%N A036801 Number of partitions satisfying (cn(0,5) <= cn(2,5) and cn(0,5) <= cn(3,5) and cn(0,5) <= cn(1,5) and cn(0,5) <= cn(4,5)).
%C A036801 For a given partition cn(i,n) means the number of its parts equal to i modulo n.
%C A036801 Short: (0<=2 and 0<=3 and 0<=1 and 0<=4).
%t A036801 okQ[p_] := Module[{c},
%t A036801 c[k_] := c[k] = Count[Mod[p, 5], k];
%t A036801 c[0] <= c[2] && c[0] <= c[3] && c[0] <= c[1] && c[0] <= c[4]];
%t A036801 a[n_] := a[n] = Count[okQ /@ IntegerPartitions[n], True];
%t A036801 Table[Print[n, " ", a[n]]; a[n], {n, 1, 45}] (* _Jean-François Alcover_, Oct 10 2024 *)
%Y A036801 Cf. A035959.
%K A036801 nonn
%O A036801 0,3
%A A036801 _Olivier Gérard_
%E A036801 a(0)=1 prepended by _Alois P. Heinz_, Oct 10 2024