A039903 Number of partitions satisfying 0 < cn(0,5) + cn(1,5) + cn(2,5) + cn(3,5) and 0 < cn(0,5) + cn(4,5) + cn(2,5) + cn(3,5).

0, 0, 1, 2, 3, 6, 9, 13, 19, 27, 40, 53, 72, 96, 130, 172, 225, 290, 376, 482, 619, 783, 990, 1242, 1561, 1945, 2421, 2992, 3697, 4545, 5583, 6819, 8321, 10113, 12279, 14851, 17940, 21597, 25971, 31140, 37289, 44531, 53115, 63199, 75108, 89063, 105481, 124672

Offset

0,4

Comments

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

Short: o < 0 + 1 + 2 + 3 and o < 0 + 4 + 2 + 3 (OMZAABBp).

Links

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

Maple

b:= proc(n, i, t, s) option remember; `if`(n=0, t*s,
      `if`(i<1, 0, b(n, i-1, t, s)+ `if`(i>n, 0,
       b(n-i, i, `if`(irem(i, 5)=4, t, 1),
      `if`(irem(i, 5)=1, s, 1)))))
    end:
a:= n-> b(n$2, 0$2):
seq(a(n), n=0..50);  # Alois P. Heinz, Apr 04 2014

Mathematica

b[n_, i_, t_, s_] := b[n, i, t, s] = If[n == 0, t*s, If[i<1, 0, b[n, i-1, t, s] + If[i>n, 0, b[n-i, i, If[Mod[i, 5] == 4, t, 1], If[Mod[i, 5] == 1, s, 1]]]]]; a[n_] := b[n, n, 0, 0]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Dec 23 2015, after Alois P. Heinz *)

Crossrefs

Sequence in context: A325340 A018347 A308824 * A357619 A360362 A280422

Adjacent sequences: A039900 A039901 A039902 * A039904 A039905 A039906

Keyword

nonn

Author

Olivier Gérard

Status

approved