A039883 Number of partitions satisfying cn(0,5) + cn(2,5) <= cn(1,5) and cn(0,5) + cn(2,5) <= cn(4,5) and cn(0,5) + cn(3,5) <= cn(1,5) and cn(0,5) + cn(3,5) <= cn(4,5).

1, 1, 1, 1, 2, 2, 3, 4, 6, 7, 10, 12, 18, 22, 27, 37, 45, 58, 74, 89, 118, 140, 177, 215, 265, 333, 397, 487, 592, 711, 881, 1041, 1263, 1507, 1803, 2185, 2578, 3080, 3656, 4321, 5185, 6062, 7193, 8450, 9931, 11772, 13706, 16105, 18827, 21945, 25817, 29880

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 <= 1 and 0 + 2 <= 4 and 0 + 3 <= 1 and 0 + 3 <= 4 (ZBBAA).

Links

Table of n, a(n) for n=0..51.

Mathematica

okQ[p_] := Module[{c},
   c[k_] := c[k] = Count[Mod[p, 5], k];
   c[0] + c[2] <= c[1] &&
   c[0] + c[2] <= c[4] &&
   c[0] + c[3] <= c[1] &&
   c[0] + 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: A122135 A339572 A027194 * A024186 A239833 A115593

Adjacent sequences: A039880 A039881 A039882 * A039884 A039885 A039886

Keyword

nonn

Author

Olivier Gérard

Extensions

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

Status

approved