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A036813
Number of partitions satisfying (cn(0,5) <= cn(1,5) = cn(4,5) and cn(0,5) <= cn(2,5) and cn(0,5) <= cn(3,5)).
0
1, 0, 1, 1, 1, 2, 2, 3, 4, 4, 8, 6, 11, 12, 14, 23, 21, 31, 37, 40, 66, 59, 87, 100, 113, 171, 162, 224, 261, 289, 431, 408, 556, 639, 714, 1017, 993, 1304, 1504, 1670, 2322, 2288, 2958, 3384, 3768, 5089, 5099, 6447, 7372, 8181, 10836, 10949, 13654, 15537
OFFSET
0,6
COMMENTS
For a given partition cn(i,n) means the number of its parts equal to i modulo n.
Short: (0<=1=4 and 0<=2 and 0<=3).
MATHEMATICA
okQ[p_] := Module[{c},
c[k_] := c[k] = Count[Mod[p, 5], k];
c[0] <= c[1] && c[1] == c[4] &&
c[0] <= c[2] && c[0] <= c[3]];
a[n_] := a[n] = Count[okQ /@ IntegerPartitions[n], True];
Table[Print[n, " ", a[n]]; a[n], {n, 1, 45}] (* Jean-François Alcover, Oct 10 2024 *)
CROSSREFS
Sequence in context: A357710 A242971 A036818 * A036814 A137776 A262699
KEYWORD
nonn
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Oct 10 2024
STATUS
approved