A244518 Number of partitions of n where the minimal multiplicity of any part is 5.

0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 1, 2, 1, 2, 3, 3, 2, 4, 2, 6, 4, 5, 4, 7, 7, 8, 8, 10, 11, 18, 13, 19, 19, 22, 29, 32, 29, 37, 37, 53, 48, 60, 54, 68, 79, 84, 86, 104, 99, 133, 125, 149, 151, 183, 191, 219, 223, 259, 268, 335, 320, 377, 391, 448, 487, 547, 552, 640, 666, 781, 795, 908, 923, 1057, 1139, 1246, 1312, 1472, 1508, 1754

Offset: 1

Author

Joerg Arndt and Alois P. Heinz, Jun 29 2014

Keywords

• nonn

Comments

Column k=5 of A243978.

Links

• Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 1..1000

Programs

Maple

b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
      b(n, i-1, k) +add(b(n-i*j, i-1, k), j=max(1, k)..n/i)))
    end:
a:= n-> b(n$2, 5) -b(n$2, 6):
seq(a(n), n=1..100);

Mathematica

b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0, b[n, i - 1, k] + Sum[b[n - i*j, i - 1, k], {j, Max[1, k], n/i}]]];
a[n_] := b[n, n, 5] - b[n, n, 6];
Array[a, 100] (* Jean-François Alcover, May 01 2018, translated from Maple *)