

A281155


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


2



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
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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



