A039902 Number of partitions satisfying 0 < cn(1,5) + cn(4,5) + cn(2,5) and 0 < cn(1,5) + cn(4,5) + cn(3,5).

0, 1, 1, 2, 4, 6, 9, 13, 19, 27, 39, 52, 71, 95, 127, 170, 220, 286, 371, 474, 614, 770, 979, 1229, 1541, 1934, 2392, 2968, 3668, 4504, 5556, 6764, 8271, 10055, 12199, 14798, 17836, 21504, 25860, 30996, 37185, 44348, 52943, 63003, 74856, 88874, 105165, 124376

Offset

0,4

Comments

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

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

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) in {0, 3}, t, 1),
      `if`(irem(i, 5) in {0, 2}, 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[MemberQ[{0, 3}, Mod[i, 5] ], t, 1], If[MemberQ[{0, 2}, Mod[i, 5]], s, 1]]]]]; a[n_] := b[n, n, 0, 0]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Nov 12 2015, after Alois P. Heinz *)

Crossrefs

Sequence in context: A164315 A171861 A039900 * A081659 A143586 A363457

Adjacent sequences: A039899 A039900 A039901 * A039903 A039904 A039905

Keyword

nonn

Author

Olivier Gérard

Status

approved