A008393 Coordination sequence for A_9 lattice.

1, 90, 2070, 22530, 151560, 731502, 2777370, 8809110, 24314490, 60110030, 135916002, 285510150, 563873400, 1056789450, 1893408750, 3262336002, 5431848930, 8774904690, 13799638910, 21186110970, 31830097752, 46894786710

Offset

0,2

Links

T. D. Noe, Table of n, a(n) for n = 0..1000

R. Bacher, P. de la Harpe and B. Venkov, Séries de croissance et séries d'Ehrhart associées aux réseaux de racines, C. R. Acad. Sci. Paris, 325 (Series 1) (1997), 1137-1142.

J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Formula

a(n) = 2 + 11*n^2*(221*n^6 + 2730*n^4 + 7917*n^2 + 5260)/2016, a(0) = 1.

G.f.: (1+x)*(1 + 80*x + 1216*x^2 + 5840*x^3 + 10036*x^4 + 5840*x^5 + 1216*x^6 + 80*x^7 + x^8)/(1-x)^9. - Colin Barker, Sep 26 2012

Maple

1, seq(2 +11*n^2*(221*n^6 +2730*n^4 +7917*n^2 +5260)/2016, n=1..40);

Mathematica

Table[11*n^2*(221*n^6 +2730*n^4 +7917*n^2 +5260)/2016 +2 -Boole[n==0], {n, 0, 40}] (* G. C. Greubel, May 27 2023 *)

Prog

(Magma) [1] cat [2 +11*n^2*(221*n^6 +2730*n^4 +7917*n^2 +5260)/2016: n in [1..40]]; // G. C. Greubel, May 27 2023
(SageMath) [11*n^2*(221*n^6 +2730*n^4 +7917*n^2 +5260)//2016 +2 -int(n==0) for n in range(41)] # G. C. Greubel, May 27 2023

Crossrefs

Row 9 of A103881.

Sequence in context: A240259 A065951 A257040 * A055603 A210090 A109124

Adjacent sequences: A008390 A008391 A008392 * A008394 A008395 A008396

Keyword

nonn,easy

Author

N. J. A. Sloane and J. H. Conway

Status

approved