A347808 Expansion of (theta_3(x) - 1)^5 / (16 * (3 - theta_3(x))).

1, 1, 1, 6, 7, 8, 19, 25, 37, 56, 76, 122, 170, 233, 347, 494, 700, 991, 1415, 2021, 2855, 4054, 5751, 8164, 11585, 16406, 23285, 33032, 46814, 66375, 94119, 133445, 189193, 268231, 380287, 539184, 764422, 1083722, 1536479, 2178349, 3088333, 4378472, 6207557

Offset: 5

Author

Ilya Gutkovskiy, Sep 14 2021

Keywords

• nonn

Comments

Number of compositions (ordered partitions) of n into 5 or more squares.

Links

• Index entries for sequences related to sums of squares

Crossrefs

Cf. A000290, A006456, A337165, A347805, A347806, A347807, A347809.

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, 5):
seq(a(n), n=5..47);  # Alois P. Heinz, Sep 14 2021

Mathematica

nmax = 47; CoefficientList[Series[(EllipticTheta[3, 0, x] - 1)^5/(16 (3 - EllipticTheta[3, 0, x])), {x, 0, nmax}], x] // Drop[#, 5] &

Formula

a(n) = Sum_{k=5..n} A337165(n,k). - Alois P. Heinz, Sep 14 2021