A281154 Expansion of (Sum_{k>=2} x^(k^2))^2.

0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 1, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 1, 0, 2, 0, 0, 0, 2

Offset

0,14

Comments

Number of ways to write n as an ordered sum of 2 squares > 1.

Links

Table of n, a(n) for n=0..104.

Index entries for sequences related to sums of squares

Formula

G.f.: (Sum_{k>=2} x^(k^2))^2.

G.f.: (1/4)*(1 + 2*x - theta_3(0,x))^2, where theta_3 is the 3rd Jacobi theta function.

Example

G.f. = x^8 + 2*x^13 + x^18 + 2*x^20 + 2*x^25 + 2*x^29 + x^32 + 2*x^34 + 2*x^40 + ...
a(13) = 2 because we have [9, 4] and [4, 9].

Mathematica

nmax = 105; CoefficientList[Series[Sum[x^k^2, {k, 2, nmax}]^2, {x, 0, nmax}], x]
CoefficientList[Series[(1 + 2 x - EllipticTheta[3, 0, x])^2/4, {x, 0, 105}], x]

Crossrefs

Cf. A000290, A000925, A004018, A006456, A063725, A078134, A085989, A280542.

Sequence in context: A328496 A035202 A227835 * A245536 A291203 A256852

Adjacent sequences: A281151 A281152 A281153 * A281155 A281156 A281157

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 16 2017

Status

approved