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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,4

COMMENTS

Number of compositions (ordered partitions) of n into 3 or more squares.

LINKS

Table of n, a(n) for n=3..47.

Index entries for sequences related to sums of 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] &

CROSSREFS

Cf. A000290, A006456, A337165, A347805, A347807, A347808, A347809.

Sequence in context: A114439 A310570 A271146 * A079257 A001609 A101590

Adjacent sequences:  A347802 A347803 A347805 * A347807 A347808 A347809

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Sep 14 2021

STATUS

approved

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Last modified October 16 20:36 EDT 2021. Contains 348047 sequences. (Running on oeis4.)