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A319815 Number of partitions of n into exactly five positive triangular numbers. 2
1, 0, 1, 0, 1, 1, 1, 1, 1, 2, 2, 2, 1, 2, 3, 2, 3, 2, 3, 3, 5, 2, 4, 4, 4, 5, 3, 5, 5, 7, 4, 5, 6, 5, 8, 6, 6, 7, 8, 6, 7, 9, 8, 8, 9, 8, 10, 10, 8, 11, 10, 9, 10, 11, 11, 12, 14, 8, 13, 14, 13, 11, 13, 14, 16, 15, 10, 16, 16, 15, 15, 16, 16, 16, 21, 12, 18 (list; graph; refs; listen; history; text; internal format)
OFFSET

5,10

LINKS

Alois P. Heinz, Table of n, a(n) for n = 5..10000

FORMULA

a(n) = [x^n y^5] 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), 5):

seq(a(n), n=5..120);

CROSSREFS

Column k=5 of A319797.

Cf. A000217.

Sequence in context: A194314 A006371 A000177 * A222656 A162545 A162544

Adjacent sequences:  A319812 A319813 A319814 * A319816 A319817 A319818

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 28 2018

STATUS

approved

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Last modified May 26 02:56 EDT 2020. Contains 334613 sequences. (Running on oeis4.)