A039898 Number of partitions satisfying 0 < cn(1,5) + cn(4,5).

0, 1, 1, 2, 4, 5, 9, 12, 18, 26, 35, 50, 67, 90, 122, 158, 212, 272, 355, 457, 582, 745, 941, 1185, 1494, 1858, 2325, 2875, 3561, 4388, 5386, 6604, 8061, 9815, 11936, 14440, 17482, 21058, 25352, 30438, 36460, 43610, 52040, 61980, 73727, 87464, 103695, 122619

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 (OMAAp).

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) in {1, 4}, 1, t)))))
    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[MemberQ[{1, 4}, Mod[i, 5]], 1, t]]]]]; a[n_] := b[n, n, 0]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Nov 12 2015, after Alois P. Heinz *)

Crossrefs

Sequence in context: A211373 A241734 A371171 * A083690 A241824 A144121

Adjacent sequences: A039895 A039896 A039897 * A039899 A039900 A039901

Keyword

nonn

Author

Olivier Gérard

Status

approved