A036815 Number of partitions satisfying (cn(0,5) = 0 and cn(2,5) = cn(3,5)).

1, 1, 1, 1, 2, 3, 4, 4, 5, 7, 11, 13, 15, 17, 23, 32, 39, 43, 51, 65, 87, 103, 117, 135, 170, 215, 255, 288, 335, 408, 507, 593, 674, 776, 934, 1130, 1318, 1492, 1716, 2032, 2428, 2805, 3180, 3634, 4264, 5021, 5777, 6526, 7441, 8641, 10083, 11529, 13011, 14763, 17029

Offset

0,5

Comments

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

Short: (0 := 0 and 2=3).

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] == 0 && c[2] == 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: A036820 A017829 A017843 * A036807 A036808 A103750

Adjacent sequences: A036812 A036813 A036814 * A036816 A036817 A036818

Keyword

nonn

Author

Olivier Gérard

Extensions

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

Status

approved