A039896 Number of partitions satisfying 0 < cn(1,5) + cn(4,5) + cn(2,5) + cn(3,5).

0, 1, 2, 3, 5, 6, 11, 15, 22, 30, 40, 56, 77, 101, 135, 173, 231, 297, 385, 490, 622, 792, 1002, 1255, 1575, 1951, 2436, 3010, 3718, 4565, 5593, 6842, 8349, 10143, 12310, 14868, 17977, 21637, 26015, 31185, 37316, 44583, 53174, 63261, 75175, 89104, 105558

Offset

0,3

Comments

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

Short: o < 1 + 4 + 2 + 3 (OMAABBpp).

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)=0, t, 1)))))
    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[Mod[i, 5] == 0, t, 1]]]]]; a[n_] := b[n, n, 0]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Apr 15 2015, after Alois P. Heinz *)

Crossrefs

Sequence in context: A187070 A038196 A039849 * A367212 A180336 A034407

Adjacent sequences: A039893 A039894 A039895 * A039897 A039898 A039899

Keyword

nonn

Author

Olivier Gérard

Status

approved