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A036806
Number of partitions satisfying (cn(0,5) = 0 and cn(2,5) <= cn(1,5) and cn(3,5) <= cn(1,5) and cn(2,5) <= cn(4,5) and cn(3,5) <= cn(4,5)).
0
1, 1, 1, 1, 2, 2, 3, 4, 6, 7, 9, 11, 17, 21, 25, 32, 40, 52, 66, 78, 99, 119, 150, 181, 221, 269, 323, 391, 472, 564, 680, 806, 964, 1141, 1359, 1608, 1902, 2237, 2632, 3096, 3637, 4254, 4974, 5792, 6771, 7870, 9158, 10611, 12299, 14247, 16460, 19016, 21922
OFFSET
0,5
COMMENTS
For a given partition cn(i,n) means the number of its parts equal to i modulo n.
Short: (0 := 0 and 2<=1 and 3<=1 and 2<=4 and 3<=4).
MATHEMATICA
okQ[p_] := Module[{c},
c[k_] := c[k] = Count[Mod[p, 5], k];
c[0] == 0 && c[2] <= c[1] &&
c[3] <= c[1] && c[2] <= c[4] &&
c[3] <= 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: A035365 A335745 A119604 * A039908 A183954 A266747
KEYWORD
nonn
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Oct 10 2024
STATUS
approved