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A347807
Expansion of (theta_3(x) - 1)^4 / (8 * (3 - theta_3(x))).
4
1, 1, 1, 5, 6, 7, 14, 19, 29, 41, 56, 88, 123, 170, 245, 351, 500, 704, 1003, 1427, 2021, 2867, 4060, 5763, 8176, 11585, 16430, 23301, 33032, 46826, 66393, 94131, 133458, 189209, 268243, 380315, 539190, 764422, 1083758, 1536495, 2178361, 3088357, 4378496, 6207581
OFFSET
4,4
COMMENTS
Number of compositions (ordered partitions) of n into 4 or more squares.
FORMULA
a(n) = Sum_{k=4..n} A337165(n,k). - Alois P. Heinz, Sep 14 2021
MAPLE
b:= proc(n, t) option remember; `if`(n=0, `if`(t=0, 1, 0), add((
s->`if`(s>n, 0, b(n-s, max(0, t-1))))(j^2), j=1..isqrt(n)))
end:
a:= n-> b(n, 4):
seq(a(n), n=4..47); # Alois P. Heinz, Sep 14 2021
MATHEMATICA
nmax = 47; CoefficientList[Series[(EllipticTheta[3, 0, x] - 1)^4/(8 (3 - EllipticTheta[3, 0, x])), {x, 0, nmax}], x] // Drop[#, 4] &
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Sep 14 2021
STATUS
approved