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A340950
Number of ways to write n as an ordered sum of 5 nonzero triangular numbers.
10
1, 0, 5, 0, 10, 5, 10, 20, 5, 35, 11, 40, 30, 35, 55, 30, 90, 25, 100, 60, 80, 120, 60, 140, 90, 161, 100, 165, 135, 165, 210, 140, 220, 180, 265, 170, 295, 200, 285, 330, 205, 365, 260, 395, 295, 391, 350, 355, 480, 340, 455, 490, 415, 480, 515, 445, 600, 510, 565, 550, 680, 545, 555
OFFSET
5,3
LINKS
FORMULA
G.f.: (theta_2(sqrt(x)) / (2 * x^(1/8)) - 1)^5, 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) 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, 5):
seq(a(n), n=5..67); # Alois P. Heinz, Jan 31 2021
MATHEMATICA
nmax = 67; CoefficientList[Series[(EllipticTheta[2, 0, Sqrt[x]]/(2 x^(1/8)) - 1)^5, {x, 0, nmax}], x] // Drop[#, 5] &
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 31 2021
STATUS
approved