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A036807
Number of partitions satisfying (cn(0,5) <= cn(2,5) = cn(3,5) and cn(0,5) <= cn(1,5) and cn(0,5) <= cn(4,5)).
0
1, 1, 1, 1, 2, 3, 4, 4, 5, 7, 11, 13, 15, 17, 23, 33, 40, 44, 52, 67, 95, 111, 125, 144, 185, 251, 292, 326, 379, 474, 633, 726, 814, 938, 1162, 1509, 1726, 1928, 2220, 2709, 3460, 3929, 4394, 5033, 6083, 7629, 8637, 9637, 11016, 13173, 16304, 18376, 20496
OFFSET
0,5
COMMENTS
For a given partition cn(i,n) means the number of its parts equal to i modulo n.
Short: (0<=2=3 and 0<=1 and 0<=4).
MATHEMATICA
okQ[p_] := Module[{c},
c[k_] := c[k] = Count[Mod[p, 5], k];
c[0] <= c[2] && c[2] == c[3] &&
c[0] <= c[1] && c[0] <= c[4]];
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: A017829 A017843 A036815 * A036808 A103750 A036805
KEYWORD
nonn
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Oct 10 2024
STATUS
approved