A036812 Number of partitions satisfying (cn(0,5) = 0 and cn(1,5) <= cn(2,5) and cn(1,5) <= cn(3,5) and cn(4,5) <= cn(2,5) and cn(4,5) <= cn(3,5)).

1, 0, 1, 1, 1, 1, 3, 2, 4, 5, 6, 9, 11, 12, 19, 22, 30, 34, 44, 54, 69, 85, 103, 122, 155, 184, 227, 271, 325, 388, 473, 557, 674, 788, 939, 1113, 1319, 1554, 1830, 2137, 2523, 2943, 3467, 4020, 4688, 5454, 6350, 7376, 8557, 9860, 11427, 13185, 15250, 17534

Offset

0,7

Comments

For a given partition cn(i,n) means the number of its parts equal to i modulo n.

Short: (0 := 0 and 1<=2 and 1<=3 and 4<=2 and 4<=3).

Links

Table of n, a(n) for n=0..53.

Mathematica

okQ[p_] := Module[{c},
   c[k_] := c[k] = Count[Mod[p, 5], k];
   c[0] == 0 && c[1] <= c[2] &&
   c[1] <= c[3] && c[4] <= c[2] &&
   c[4] <= 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: A216249 A113004 A113001 * A039906 A056011 A117123

Adjacent sequences: A036809 A036810 A036811 * A036813 A036814 A036815

Keyword

nonn

Author

Olivier Gérard

Extensions

a(0)=1 prepended by Alois P. Heinz, Oct 10 2024

Status

approved