A036816 Number of partitions satisfying (cn(0,5) <= cn(2,5) = cn(3,5) and cn(2,5) <= cn(1,5) and cn(2,5) <= cn(4,5)).

1, 1, 1, 1, 2, 2, 3, 3, 4, 5, 7, 8, 10, 11, 14, 21, 24, 26, 31, 39, 60, 65, 72, 82, 107, 155, 170, 185, 214, 271, 383, 419, 459, 525, 660, 896, 987, 1078, 1234, 1524, 2024, 2221, 2437, 2775, 3391, 4403, 4832, 5296, 6024, 7271, 9304, 10180, 11168, 12650, 15146

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 2<=1 and 2<=4).

Links

Table of n, a(n) for n=0..54.

Mathematica

okQ[p_] := Module[{c},
   c[k_] := c[k] = Count[Mod[p, 5], k];
   c[0] <= c[2] && c[2] == c[3] &&
   c[2] <= c[1] && c[2] <= c[4]];
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: A035380 A036823 A035575 * A367399 A113788 A018243

Adjacent sequences: A036813 A036814 A036815 * A036817 A036818 A036819

Keyword

nonn

Author

Olivier Gérard

Extensions

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

Status

approved