A039904 Number of partitions satisfying 0 < cn(0,5) + cn(1,5) + cn(4,5) + cn(2,5) and 0 < cn(0,5) + cn(1,5) + cn(4,5) + cn(3,5).

0, 1, 1, 2, 4, 7, 9, 14, 20, 28, 41, 54, 74, 99, 131, 174, 226, 294, 380, 485, 623, 785, 996, 1249, 1565, 1952, 2425, 3001, 3707, 4553, 5592, 6828, 8334, 10128, 12291, 14866, 17954, 21617, 25991, 31159, 37311, 44554, 53141, 63229, 75137, 89096, 105515, 124711

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 + 4 + 2 and o < 0 + 1 + 4 + 3 (OMZBBAAp).

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)=2, t, 1),
      `if`(irem(i, 5)=3, 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] == 2, t, 1], If[Mod[i, 5] == 3, 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: A139533 A227116 A180742 * A115162 A278977 A097433

Adjacent sequences: A039901 A039902 A039903 * A039905 A039906 A039907

Keyword

nonn

Author

Olivier Gérard

Status

approved