A319223 Number of ordered ways of writing n^3 as a sum of n squares.

1, 2, 4, 32, 24, 14112, 674368, 39801344, 2454266992, 166591027058, 12820702401872, 1156778646258336, 119773060481140800, 14004241350957965408, 1791476464655904407168, 247572699435320047056384, 36696694077934168215974368, 5825316759916541565549586176, 989291135292653632945527984868

Offset: 0

Author

Ilya Gutkovskiy, Sep 13 2018

Keywords

• nonn

Links

• Index entries for sequences related to sums of squares

Crossrefs

Cf. A000290, A000578, A066535, A218494, A232173, A298671, A298938, A298939.

Programs

Mathematica

Table[SeriesCoefficient[EllipticTheta[3, 0, x]^n, {x, 0, n^3}], {n, 0, 18}]
Join[{1}, Table[SquaresR[n, n^3], {n, 18}]]

Formula

a(n) = [x^(n^3)] theta_3(x)^n, where theta_3() is the Jacobi theta function.

a(n) = [x^(n^3)] (Sum_{k=-infinity..infinity} x^(k^2))^n.