A319818 Number of partitions of n into exactly eight positive triangular numbers.

1, 0, 1, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 4, 3, 4, 3, 4, 5, 6, 4, 6, 6, 7, 7, 7, 8, 9, 11, 9, 10, 11, 11, 14, 13, 13, 15, 16, 15, 18, 18, 18, 19, 22, 20, 22, 25, 23, 27, 26, 26, 29, 29, 32, 32, 36, 31, 37, 39, 37, 39, 42, 41, 47, 48, 44, 48, 52, 52, 54, 55, 55

Offset

8,10

Links

Alois P. Heinz, Table of n, a(n) for n = 8..10000

Formula

a(n) = [x^n y^8] 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), 8):
seq(a(n), n=8..120);

Crossrefs

Column k=8 of A319797.

Cf. A000217.

Sequence in context: A164296 A319817 A233566 * A319819 A319820 A319799

Adjacent sequences: A319815 A319816 A319817 * A319819 A319820 A319821

Keyword

nonn

Author

Alois P. Heinz, Sep 28 2018

Status

approved