A039897 Number of partitions satisfying 0 < cn(2,5) + cn(3,5).

0, 0, 1, 2, 3, 4, 7, 11, 17, 23, 32, 44, 63, 85, 114, 149, 198, 260, 341, 436, 559, 712, 910, 1149, 1446, 1803, 2254, 2803, 3478, 4282, 5267, 6453, 7905, 9635, 11716, 14191, 17180, 20735, 24985, 29998, 35965, 43019, 51404, 61257, 72880, 86510, 102580, 121405

Offset

0,4

Comments

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

Short: o < 2 + 3 (OMBBp).

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Maple

b:= proc(n, i, t) option remember; `if`(n=0, t,
      `if`(i<1, 0, b(n, i-1, t)+ `if`(i>n, 0,
       b(n-i, i, `if`(irem(i, 5) in {2, 3}, 1, t)))))
    end:
a:= n-> b(n$2, 0):
seq(a(n), n=0..50);  # Alois P. Heinz, Apr 04 2014

Mathematica

b[n_, i_, t_] := b[n, i, t] = If[n == 0, t, If[i<1, 0, b[n, i-1, t] + If[i > n, 0, b[n-i, i, If[2 <= Mod[i, 5] <= 3, 1, t]]]]]; a[n_] := b[n, n, 0]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Nov 12 2015, after Alois P. Heinz *)

Crossrefs

Sequence in context: A221997 A221998 A165407 * A297789 A222122 A222024

Adjacent sequences: A039894 A039895 A039896 * A039898 A039899 A039900

Keyword

nonn

Author

Olivier Gérard

Status

approved