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A055427 Number of points in Z^n of norm <= 3. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
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
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified July 21 06:08 EDT 2024. Contains 374463 sequences. (Running on oeis4.)