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A055412 Number of points in Z^6 of norm <= n. 6
1, 13, 485, 4197, 23793, 84769, 252673, 622573, 1395261, 2787125, 5260181, 9249417, 15637897, 25112577, 39258381, 59174749, 87380293, 125264525, 176663297, 244000537, 332379769, 444344469, 587923621, 766764301, 990981473 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..500

FORMULA

a(n) = A122510(6,n^2). - R. J. Mathar, Apr 21 2010

a(n) = [x^(n^2)] theta_3(x)^6/(1 - x), where theta_3() is the Jacobi theta function. - Ilya Gutkovskiy, Apr 14 2018

MATHEMATICA

t[d_, n_] := t[d, n] = t[d, n - 1] + SquaresR[d, n]; t[d_, 0] = 1;

a[n_] := t[6, n^2];

a /@ Range[0, 100] (* Jean-Fran├žois Alcover, Sep 27 2019, after R. J. Mathar *)

CROSSREFS

Column k=6 of A302997.

Cf. A122510.

Sequence in context: A173403 A220560 A033983 * A196911 A197078 A116114

Adjacent sequences:  A055409 A055410 A055411 * A055413 A055414 A055415

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified January 22 21:47 EST 2022. Contains 350504 sequences. (Running on oeis4.)