A244517 Number of partitions of n where the minimal multiplicity of any part is 4.

0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 1, 2, 1, 4, 2, 3, 3, 6, 3, 6, 4, 10, 6, 10, 7, 19, 13, 17, 16, 31, 22, 34, 28, 48, 39, 54, 49, 76, 62, 84, 79, 120, 96, 133, 124, 179, 162, 202, 193, 275, 249, 315, 300, 412, 379, 480, 467, 603, 577, 711, 696, 905, 850, 1035, 1038, 1307, 1258, 1509, 1511, 1864, 1834, 2185, 2171, 2673, 2636

Offset

1,12

Comments

Column k=4 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, 4) -b(n$2, 5):
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, 4] - b[n, n, 5];
Array[a, 100] (* Jean-François Alcover, May 01 2018, translated from Maple *)

Crossrefs

Sequence in context: A353645 A249029 A075997 * A297294 A161309 A161243

Adjacent sequences: A244514 A244515 A244516 * A244518 A244519 A244520

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jun 29 2014

Status

approved