A319817 Number of partitions of n into exactly seven positive triangular numbers.

1, 0, 1, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 4, 3, 3, 3, 4, 4, 6, 4, 5, 5, 7, 6, 6, 8, 7, 10, 8, 8, 10, 10, 11, 11, 12, 11, 14, 14, 13, 14, 16, 15, 17, 18, 17, 20, 19, 20, 21, 22, 21, 22, 27, 23, 28, 26, 26, 29, 31, 27, 31, 34, 34, 35, 34, 34, 37, 42, 37, 39, 42

Offset: 7

Author

Alois P. Heinz, Sep 28 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 7..10000

Crossrefs

Column k=7 of A319797.

Cf. A000217.

Programs

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 b(n, h(n), 7):
seq(a(n), n=7..120);

Formula

a(n) = [x^n y^7] 1/Product_{j>=1} (1-y*x^A000217(j)).