A319816 Number of partitions of n into exactly six positive triangular numbers.

1, 0, 1, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 2, 4, 4, 5, 3, 5, 4, 6, 6, 4, 7, 6, 8, 7, 7, 7, 8, 10, 7, 10, 10, 10, 10, 11, 10, 12, 13, 12, 13, 14, 14, 14, 16, 14, 16, 16, 14, 20, 19, 18, 17, 21, 18, 22, 21, 20, 22, 26, 23, 21, 25, 24, 29, 26, 23, 29, 30

Offset

6,10

Links

Alois P. Heinz, Table of n, a(n) for n = 6..10000

Formula

a(n) = [x^n y^6] 1/Product_{j>=1} (1-y*x^A000217(j)).

Maple

h:= proc(n) option remember; `if`(n<1, 0,
      `if`(issqr(8*n+1), n, h(n-1)))
    end:
b:= proc(n, i, k) option remember; `if`(n=0, `if`(k=0, 1, 0), `if`(
      k>n or i*k<n, 0, b(n, h(i-1), k)+b(n-i, h(min(n-i, i)), k-1)))
    end:
a:= n-> b(n, h(n), 6):
seq(a(n), n=6..120);

Crossrefs

Column k=6 of A319797.

Cf. A000217.

Sequence in context: A137921 A064876 A262689 * A343437 A348242 A105517

Adjacent sequences: A319813 A319814 A319815 * A319817 A319818 A319819

Keyword

nonn

Author

Alois P. Heinz, Sep 28 2018

Status

approved