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A008393 Coordination sequence for A_9 lattice.

%I A008393 #29 May 30 2023 14:11:30
%S A008393 1,90,2070,22530,151560,731502,2777370,8809110,24314490,60110030,
%T A008393 135916002,285510150,563873400,1056789450,1893408750,3262336002,
%U A008393 5431848930,8774904690,13799638910,21186110970,31830097752,46894786710
%N A008393 Coordination sequence for A_9 lattice.
%H A008393 T. D. Noe, <a href="/A008393/b008393.txt">Table of n, a(n) for n = 0..1000</a>
%H A008393 R. Bacher, P. de la Harpe and B. Venkov, <a href="https://doi.org/10.1016/S0764-4442(97)83542-2">Séries de croissance et séries d'Ehrhart associées aux réseaux de racines</a>, C. R. Acad. Sci. Paris, 325 (Series 1) (1997), 1137-1142.
%H A008393 J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (<a href="http://neilsloane.com/doc/Me220.pdf">pdf</a>).
%H A008393 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).
%F A008393 a(n) = 2 + 11*n^2*(221*n^6 + 2730*n^4 + 7917*n^2 + 5260)/2016, a(0) = 1.
%F A008393 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
%p A008393 1, seq(2 +11*n^2*(221*n^6 +2730*n^4 +7917*n^2 +5260)/2016, n=1..40);
%t A008393 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 *)
%o A008393 (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
%o A008393 (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
%Y A008393 Row 9 of A103881.
%K A008393 nonn,easy
%O A008393 0,2
%A A008393 _N. J. A. Sloane_ and _J. H. Conway_