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
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).
Crossrefs
Row 9 of A103881.
Programs
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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
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Maple
1, seq(2 +11*n^2*(221*n^6 +2730*n^4 +7917*n^2 +5260)/2016, n=1..40);
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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 *) -
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
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