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Number of partitions satisfying cn(0,5) <= cn(1,5) and cn(0,5) <= cn(4,5).
0

%I #10 Oct 11 2024 06:55:54

%S 1,1,2,3,5,6,10,13,19,25,35,45,62,79,105,136,176,223,288,361,462,575,

%T 725,899,1123,1388,1715,2108,2592,3160,3872,4694,5712,6905,8348,10059,

%U 12101,14514,17397,20774,24822,29518,35131,41664,49378,58416,68982,81341,95810,112595,132299,155027,181623,212345,248042

%N Number of partitions satisfying cn(0,5) <= cn(1,5) and cn(0,5) <= 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 and 0 <= 4 (AA).

%t okQ[p_] := Module[{c},

%t c[k_] := c[k] = Count[Mod[p, 5], k];

%t c[0] <= c[1] && c[0] <= c[4]];

%t a[n_] := a[n] = Count[okQ /@ IntegerPartitions[n], True];

%t Table[Print[n, " ", a[n]]; a[n], {n, 0, 54}] (* _Jean-François Alcover_, Oct 11 2024 *)

%K nonn

%O 0,3

%A _Olivier Gérard_

%E a(0)=1 prepended by _Jean-François Alcover_, Oct 11 2024