A319820 Number of partitions of n into exactly ten positive triangular numbers.

1, 0, 1, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 4, 3, 4, 3, 5, 5, 7, 5, 6, 7, 8, 8, 8, 10, 10, 12, 12, 11, 14, 14, 16, 16, 17, 18, 20, 21, 21, 23, 25, 24, 29, 29, 29, 32, 33, 35, 36, 39, 38, 41, 47, 44, 50, 48, 52, 55, 58, 55, 62, 66, 66, 70, 71, 72, 78, 84, 82, 84

Offset

10,10

Links

Alois P. Heinz, Table of n, a(n) for n = 10..10000

Formula

a(n) = [x^n y^10] 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), 10):
seq(a(n), n=10..120);

Crossrefs

Column k=10 of A319797.

Cf. A000217.

Sequence in context: A233566 A319818 A319819 * A319799 A294078 A064133

Adjacent sequences: A319817 A319818 A319819 * A319821 A319822 A319823

Keyword

nonn

Author

Alois P. Heinz, Sep 28 2018

Status

approved