The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #10 Oct 11 2024 10:18:47
%S 0,1,2,3,4,7,10,15,21,30,41,56,74,101,134,177,228,297,382,493,626,794,
%T 999,1260,1575,1967,2439,3022,3724,4587,5618,6874,8374,10189,12351,
%U 14953,18041,21740,26116,31329,37483,44793,53392,63555,75482,75482,89537,105998,125326,147885,174295,205071,241000,282758
%N Number of partitions satisfying cn(0,5) < cn(2,5) + cn(3,5).
%C For a given partition cn(i,n) means the number of its parts equal to i modulo n.
%C Short: 0 < 2 + 3 (ZMBBp).
%t okQ[p_] := Module[{c},
%t c[k_] := c[k] = Count[Mod[p, 5], k];
%t c[0] < c[2] + c[3]];
%t a[n_] := a[n] = Count[okQ /@ IntegerPartitions[n], True];
%t Table[Print[n, " ", a[n]]; a[n], {n, 1, 53}] (* _Jean-François Alcover_, Oct 11 2024 *)
%K nonn
%O 1,3
%A _Olivier Gérard_