A039901 Number of partitions satisfying 0 < cn(1,5) + cn(2,5) + cn(3,5) and 0 < cn(4,5) + cn(2,5) + cn(3,5).

0, 0, 1, 2, 3, 5, 8, 12, 18, 25, 37, 49, 68, 91, 123, 165, 215, 278, 362, 465, 603, 760, 962, 1209, 1524, 1911, 2374, 2934, 3629, 4471, 5514, 6728, 8208, 9982, 12139, 14720, 17772, 21390, 25732, 30889, 37049, 44231, 52749, 62782, 74671, 88640

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 + 2 + 3 and o < 4 + 2 + 3 (OMAABBp).

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, 4}, t, 1),
      `if`(irem(i, 5) in {0, 1}, s, 1)))))
    end:
a:= n-> b(n$2, 0$2):
seq(a(n), n=0..50);  # Alois P. Heinz, Apr 03 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, 4}, Mod[i, 5]], t, 1], If[MemberQ[{0, 1}, 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: A299731 A252864 A039899 * A173564 A121946 A241823

Adjacent sequences: A039898 A039899 A039900 * A039902 A039903 A039904

Keyword

nonn

Author

Olivier Gérard

Status

approved