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%I #10 Oct 11 2024 12:53:00
%S 1,1,2,4,5,8,12,17,24,34,45,63,84,111,148,193,251,326,417,536,678,862,
%T 1083,1360,1701,2116,2624,3248,3996,4915,6015,7349,8948,10875,13171,
%U 15932,19207,23121,27760,33274,39789,47504,56592,67320,79909,94738,112079,132436,156212,183998,216399,254166,298066,349148
%N Number of partitions satisfying cn(0,5) < cn(1,5) + cn(4,5).
%C For a given partition cn(i,n) means the number of its parts equal to i modulo n.
%C Short: 0 < 1 + 4 (ZMAAp).
%t okQ[p_] := Module[{c},
%t c[k_] := c[k] = Count[Mod[p, 5], k];
%t c[0] < c[1] + c[4]];
%t a[n_] := a[n] = Count[okQ /@ IntegerPartitions[n], True];
%t Table[Print[n, " ", a[n]]; a[n], {n, 1, 54}] (* _Jean-François Alcover_, Oct 11 2024 *)
%K nonn
%O 1,3
%A _Olivier Gérard_