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URL: https://oeis.org/A347806

⇱ A347806 - OEIS

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A347806
Expansion of (theta_3(x) - 1)^3 / (4 * (3 - theta_3(x))).
4
1, 1, 1, 4, 5, 6, 10, 14, 22, 30, 41, 62, 88, 123, 173, 248, 354, 500, 710, 1006, 1427, 2024, 2867, 4066, 5767, 8176, 11591, 16436, 23301, 33032, 46832, 66396, 94137, 133461, 189209, 268252, 380315, 539190, 764431, 1083764, 1536498, 2178364, 3088363, 4378502, 6207581
OFFSET
3,4
COMMENTS
Number of compositions (ordered partitions) of n into 3 or more squares.
FORMULA
a(n) = Sum_{k=3..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, 3):
seq(a(n), n=3..47); # Alois P. Heinz, Sep 14 2021
MATHEMATICA
nmax = 47; CoefficientList[Series[(EllipticTheta[3, 0, x] - 1)^3/(4 (3 - EllipticTheta[3, 0, x])), {x, 0, nmax}], x] // Drop[#, 3] &
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Sep 14 2021
STATUS
approved