A036803 Number of partitions satisfying (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, 2, 3, 3, 5, 6, 9, 12, 15, 18, 26, 33, 45, 52, 67, 86, 111, 142, 170, 207, 267, 327, 414, 492, 598, 740, 909, 1110, 1333, 1588, 1940, 2339, 2831, 3363, 3997, 4790, 5736, 6836, 8108, 9533, 11326, 13409, 15863, 18662, 21862, 25683, 30212, 35425, 41476

Offset

0,6

Comments

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

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

Links

Table of n, a(n) for n=0..52.

Mathematica

okQ[p_] := Module[{c},
   c[k_] := c[k] = Count[Mod[p, 5], k];
   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: A070830 A039862 A018051 * A179492 A230580 A241409

Adjacent sequences: A036800 A036801 A036802 * A036804 A036805 A036806

Keyword

nonn

Author

Olivier Gérard

Extensions

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

Status

approved