A055427 Number of points in Z^n of norm <= 3.

1, 7, 29, 123, 425, 1343, 4197, 12435, 33809, 84663, 198765, 444907, 959801, 2005615, 4064821, 7988867, 15221537, 28122727, 50423741, 87851099, 148962249, 246243487, 397527813, 627798387, 971451697, 1475103511, 2201030157

Offset

0,2

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (10, -45, 120, -210, 252, -210, 120, -45, 10, -1).

Formula

Appears to satisfy a 9-degree polynomial. - Ralf Stephan, Mar 07 2004

Empirical g.f.: (x+1)*(93*x^8+620*x^7-848*x^6+516*x^5-150*x^4+20*x^3+8*x^2-4*x+1) / (x-1)^10. - Colin Barker, Jul 07 2013

Above conjectures confirmed by later additions of b-file from Andrew Howroyd and program from Jean-François Alcover with connection to A302997. - Ray Chandler, Jun 27 2024

Mathematica

a[n_] := SeriesCoefficient[1/(1-x) Sum[x^(i^2), {i, -3, 3}]^n, {x, 0, 9}];
a /@ Range[0, 26] (* Jean-François Alcover, Sep 29 2019, from A302997 *)

Crossrefs

Row n=3 of A302997.

Sequence in context: A066744 A037576 A327587 * A048876 A126394 A252832

Adjacent sequences: A055424 A055425 A055426 * A055428 A055429 A055430

Keyword

nonn

Author

David W. Wilson

Status

approved