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A340952 Number of ways to write n as an ordered sum of 7 nonzero triangular numbers. 9
1, 0, 7, 0, 21, 7, 35, 42, 35, 112, 42, 182, 112, 210, 260, 217, 462, 252, 651, 399, 728, 777, 672, 1232, 749, 1533, 1127, 1659, 1617, 1792, 2289, 1890, 2926, 2212, 3339, 2990, 3584, 3654, 4046, 4613, 4263, 5754, 4487, 6636, 5733, 6825, 7014, 7203, 8617, 7560, 10087, 8302 (list; graph; refs; listen; history; text; internal format)
OFFSET
7,3
LINKS
FORMULA
G.f.: (theta_2(sqrt(x)) / (2 * x^(1/8)) - 1)^7, 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, 7):
seq(a(n), n=7..58); # Alois P. Heinz, Jan 31 2021
MATHEMATICA
nmax = 58; CoefficientList[Series[(EllipticTheta[2, 0, Sqrt[x]]/(2 x^(1/8)) - 1)^7, {x, 0, nmax}], x] // Drop[#, 7] &
CROSSREFS
Sequence in context: A052440 A246919 A167299 * A282071 A064854 A199917
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 31 2021
STATUS
approved

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Last modified February 29 03:50 EST 2024. Contains 370401 sequences. (Running on oeis4.)