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A319820
Number of partitions of n into exactly ten positive triangular numbers.
5
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
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 28 2018
STATUS
approved