A319819 Number of partitions of n into exactly nine positive triangular numbers.

1, 0, 1, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 4, 3, 4, 3, 5, 5, 6, 5, 6, 6, 8, 8, 7, 9, 10, 11, 11, 11, 12, 13, 15, 14, 16, 17, 17, 19, 20, 19, 23, 23, 24, 25, 27, 27, 28, 33, 30, 33, 34, 34, 41, 39, 41, 41, 46, 44, 49, 50, 49, 54, 59, 56, 58, 63, 63, 68, 70, 67

Offset

9,10

Links

Alois P. Heinz, Table of n, a(n) for n = 9..10000

Formula

a(n) = [x^n y^9] 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), 9):
seq(a(n), n=9..120);

Crossrefs

Column k=9 of A319797.

Cf. A000217.

Sequence in context: A319817 A233566 A319818 * A319820 A319799 A294078

Adjacent sequences: A319816 A319817 A319818 * A319820 A319821 A319822

Keyword

nonn

Author

Alois P. Heinz, Sep 28 2018

Status

approved