

A319819


Number of partitions of n into exactly nine positive triangular numbers.


5



1, 0, 1, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 4, 3, 4, 3, 5, 5, 6, 5, 6, 6, 8, 8, 7, 9, 10, 11, 11, 11, 12, 13, 15, 14, 16, 17, 17, 19, 20, 19, 23, 23, 24, 25, 27, 27, 28, 33, 30, 33, 34, 34, 41, 39, 41, 41, 46, 44, 49, 50, 49, 54, 59, 56, 58, 63, 63, 68, 70, 67
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OFFSET

9,10


LINKS



FORMULA

a(n) = [x^n y^9] 1/Product_{j>=1} (1y*x^A000217(j)).


MAPLE

h:= proc(n) option remember; `if`(n<1, 0,
`if`(issqr(8*n+1), n, h(n1)))
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(i1), k)+b(ni, h(min(ni, i)), k1)))
end:
a:= n> b(n, h(n), 9):
seq(a(n), n=9..120);


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



