A036824 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)).

1, 0, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 6, 6, 8, 10, 11, 13, 16, 17, 26, 24, 32, 36, 42, 60, 57, 74, 86, 93, 141, 127, 171, 193, 213, 306, 289, 373, 428, 465, 655, 623, 802, 906, 995, 1348, 1320, 1652, 1877, 2050, 2723, 2696, 3334, 3761, 4131, 5355, 5380, 6543, 7381, 8087, 10353, 10447, 12598, 14150, 15520, 19596

Offset

0,7

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).

Links

Alois P. Heinz, Table of n, a(n) for n = 0..100

Mathematica

okQ[p_] := Module[{c},
   c[k_] := c[k] = Count[Mod[p, 5], k];
   c[0] == 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, 0, 54}] (* Jean-François Alcover, Oct 11 2024 *)

Crossrefs

Sequence in context: A342096 A210716 A027190 * A108104 A173091 A029025

Adjacent sequences: A036821 A036822 A036823 * A036825 A036826 A036827

Keyword

nonn

Author

Olivier Gérard

Extensions

a(0)=1 prepended by Jean-François Alcover, Oct 11 2024

Status

approved