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

7,10

Links

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

Formula

a(n) = [x^n y^7] 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), 7):
seq(a(n), n=7..120);

Crossrefs

Column k=7 of A319797.

Cf. A000217.

Sequence in context: A260123 A319411 A164296 * A233566 A319818 A319819

Adjacent sequences: A319814 A319815 A319816 * A319818 A319819 A319820

Keyword

nonn

Author

Alois P. Heinz, Sep 28 2018

Status

approved