A347805 Expansion of (theta_3(x) - 1)^2 / (2 * (3 - theta_3(x))).

1, 1, 1, 3, 4, 5, 7, 10, 16, 22, 30, 43, 62, 88, 123, 175, 249, 354, 502, 710, 1006, 1427, 2024, 2869, 4068, 5767, 8176, 11593, 16436, 23301, 33033, 46832, 66398, 94137, 133461, 189211, 268252, 380315, 539192, 764433, 1083764, 1536498, 2178364, 3088365, 4378502, 6207581, 8800750

Offset

2,4

Comments

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

Links

Table of n, a(n) for n=2..48.

Index entries for sequences related to sums of squares

Formula

From Alois P. Heinz, Sep 14 2021: (Start)

a(n) = A006456(n) - A010052(n).

a(n) = Sum_{k=2..n} A337165(n,k). (End)

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, 2):
seq(a(n), n=2..48);  # Alois P. Heinz, Sep 14 2021

Mathematica

nmax = 48; CoefficientList[Series[(EllipticTheta[3, 0, x] - 1)^2/(2 (3 - EllipticTheta[3, 0, x])), {x, 0, nmax}], x] // Drop[#, 2] &

Crossrefs

Cf. A000290, A006456, A010052, A033985, A219610, A337165, A347806, A347807, A347808, A347809.

Sequence in context: A162311 A003312 A022440 * A088130 A046840 A057773

Adjacent sequences: A347802 A347803 A347804 * A347806 A347807 A347808

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 14 2021

Status

approved