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%I #10 Oct 10 2024 15:16:28
%S 1,0,1,1,1,2,2,3,4,4,8,6,11,12,14,24,21,31,37,40,69,59,87,100,112,178,
%T 160,223,259,284,443,399,549,629,694,1035,961,1277,1467,1609,2339,
%U 2195,2874,3276,3601,5084,4854,6222,7088,7767,10745,10358,13100,14854
%N Number of partitions satisfying (cn(1,5) = cn(4,5) and cn(1,5) <= cn(2,5) and cn(1,5) <= cn(3,5)).
%C For a given partition cn(i,n) means the number of its parts equal to i modulo n.
%C Short: (1=4 and 1<=2 and 1<=3).
%t okQ[p_] := Module[{c},
%t c[k_] := c[k] = Count[Mod[p, 5], k];
%t c[1] == c[4] && c[1] <= c[2] && c[1] <= c[3]];
%t a[n_] := a[n] = Count[okQ /@ IntegerPartitions[n], True];
%t Table[Print[n, " ", a[n]]; a[n], {n, 1, 45}] (* _Jean-François Alcover_, Oct 10 2024 *)
%K nonn
%O 0,6
%A _Olivier Gérard_
%E a(0)=1 prepended by _Alois P. Heinz_, Oct 10 2024