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

1,15

Comments

Column k=5 of A243978.

Links

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

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 *)

Crossrefs

Sequence in context: A242552 A249717 A249718 * A367251 A161310 A161244

Adjacent sequences: A244515 A244516 A244517 * A244519 A244520 A244521

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jun 29 2014

Status

approved