[go: up one dir, main page]

login
A008393
Coordination sequence for A_9 lattice.
2
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
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
KEYWORD
nonn,easy
STATUS
approved