A347809 Expansion of (theta_3(x) - 1)^6 / (32 * (3 - theta_3(x))).

1, 1, 1, 7, 8, 9, 25, 32, 46, 76, 102, 165, 233, 317, 488, 690, 971, 1395, 1991, 2850, 4024, 5721, 8144, 11550, 16396, 23225, 32987, 46814, 66315, 94069, 133415, 189148, 268181, 380227, 539114, 764387, 1083692, 1536369, 2178299, 3088302, 4378362, 6207477

Offset: 6

Author

Ilya Gutkovskiy, Sep 14 2021

Keywords

• nonn

Comments

Number of compositions (ordered partitions) of n into 6 or more squares.

Links

• Index entries for sequences related to sums of squares

Crossrefs

Cf. A000290, A006456, A337165, A347805, A347806, A347807, A347808.

Programs

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, 6):
seq(a(n), n=6..47);  # Alois P. Heinz, Sep 14 2021

Mathematica

nmax = 47; CoefficientList[Series[(EllipticTheta[3, 0, x] - 1)^6/(32 (3 - EllipticTheta[3, 0, x])), {x, 0, nmax}], x] // Drop[#, 6] &

Formula

a(n) = Sum_{k=6..n} A337165(n,k). - Alois P. Heinz, Sep 14 2021