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A340954
Number of ways to write n as an ordered sum of 9 nonzero triangular numbers.
9
1, 0, 9, 0, 36, 9, 84, 72, 126, 261, 162, 576, 336, 882, 873, 1092, 1845, 1386, 3061, 2160, 4167, 3957, 4860, 6948, 5580, 10287, 7812, 12777, 12276, 14634, 18363, 17136, 25056, 21282, 31266, 28899, 36075, 39654, 41202, 51348, 49383, 63270, 59391, 76059, 73611, 87319, 93582, 96966
OFFSET
9,3
LINKS
FORMULA
G.f.: (theta_2(sqrt(x)) / (2 * x^(1/8)) - 1)^9, where theta_2() is the Jacobi theta function.
MAPLE
b:= proc(n, k) option remember; local r, t, d; r, t, d:= $0..2;
if n=0 then `if`(k=0, 1, 0) elif k<1 then 0 else
while t<=n do r:= r+b(n-t, k-1); t, d:= t+d, d+1 od; r fi
end:
a:= n-> b(n, 9):
seq(a(n), n=9..56); # Alois P. Heinz, Jan 31 2021
MATHEMATICA
nmax = 56; CoefficientList[Series[(EllipticTheta[2, 0, Sqrt[x]]/(2 x^(1/8)) - 1)^9, {x, 0, nmax}], x] // Drop[#, 9] &
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 31 2021
STATUS
approved