A347807 Expansion of (theta_3(x) - 1)^4 / (8 * (3 - theta_3(x))).

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.

Links

Table of n, a(n) for n=4..47.

Index entries for sequences related to sums of 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] &

Crossrefs

Cf. A000290, A006456, A337165, A347805, A347806, A347808, A347809.

Sequence in context: A111018 A326132 A342630 * A161925 A078694 A221175

Adjacent sequences: A347804 A347805 A347806 * A347808 A347809 A347810

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 14 2021

Status

approved