A281155 Expansion of (Sum_{k>=2} x^(k^2))^3.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 3, 0, 0, 0, 0, 3, 0, 3, 0, 0, 1, 0, 6, 0, 0, 0, 3, 3, 0, 3, 0, 6, 0, 0, 3, 0, 3, 3, 6, 0, 0, 1, 6, 6, 0, 0, 0, 6, 0, 6, 6, 0, 3, 0, 6, 6, 0, 0, 6, 3, 3, 3, 6, 6, 0, 3, 0, 6, 1, 3, 12, 6, 0, 0, 6, 3, 6, 6, 0, 3, 0, 3, 15, 6, 0, 0, 6, 12, 0, 3, 3, 6, 6, 0, 12, 3, 0, 6, 6

Offset

0,18

Comments

Number of ways to write n as an ordered sum of 3 squares > 1.

Links

Table of n, a(n) for n=0..105.

Index entries for sequences related to sums of squares

Formula

G.f.: (Sum_{k>=2} x^(k^2))^3.

G.f.: (1/8)*(-1 - 2*x + theta_3(0,x))^3, where theta_3 is the 3rd Jacobi theta function.

Example

G.f. = x^12 + 3*x^17 + 3*x^22 + 3*x^24 + x^27 + 6*x^29 + 3*x^33 + 3*x^34 + 3*x^36 + ...
a(17) = 3 because we have [9, 4, 4], [4, 9, 4] and [4, 4, 9].

Mathematica

nmax = 105; CoefficientList[Series[Sum[x^k^2, {k, 2, nmax}]^3, {x, 0, nmax}], x]
CoefficientList[Series[(-1 - 2 x + EllipticTheta[3, 0, x])^3/8, {x, 0, 105}], x]

Crossrefs

Cf. A000290, A005875, A002102, A006456, A063691, A078134, A280542.

Sequence in context: A325675 A279948 A264009 * A321432 A220093 A097017

Adjacent sequences: A281152 A281153 A281154 * A281156 A281157 A281158

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 16 2017

Status

approved