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%I #31 Sep 06 2023 01:37:24
%S 1,162,5154,67266,507906,2653346,10666146,35310402,100746498,
%T 255708578,590675490,1262903490,2531446530,4804547490,8702041250,
%U 15135668034,25410452994,41350565538,65453329442,101075312322,152654680578,225974263458,328470027426,469589919554
%N Coordination sequence for root lattice B_9.
%H Vincenzo Librandi, <a href="/A022151/b022151.txt">Table of n, a(n) for n = 0..1000</a>
%H M. Baake and U. Grimm, <a href="https://arxiv.org/abs/cond-mat/9706122">Coordination sequences for root lattices and related graphs</a>, arXiv:cond-mat/9706122, Zeit. f. Kristallographie, 212 (1997), 253-256.
%H R. Bacher, P. de la Harpe and B. Venkov, <a href="http://dx.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 <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 a(0)=1; for n>0, a(n) = ( 2012*n^8 - 3952*n^7 + 27160*n^6 - 35392*n^5 + 81508*n^4 - 57568*n^3 + 45560*n^2 - 8928*n + 630 ) / 315. - _Ralf Stephan_, Apr 28 2004
%F G.f.: -(x^9 +825*x^8 +11124*x^7 +49380*x^6 +91118*x^5 +74574*x^4 +26628*x^3 +3732*x^2 +153*x +1)/(x -1)^9. - _Colin Barker_, Nov 18 2012
%t CoefficientList[Series[-(x^9 + 825 x^8 + 11124 x^7 + 49380 x^6 + 91118 x^5 + 74574 x^4 + 26628 x^3 + 3732 x^2 + 153 x + 1)/(x - 1)^9, {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 17 2013 *)
%t Join[{1},LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{162,5154,67266,507906,2653346,10666146,35310402,100746498,255708578},30]] (* _Harvey P. Dale_, Mar 23 2015 *)
%o (Magma) [1] cat [(2012*n^8-3952*n^7+27160*n^6-35392*n^5+81508*n^4-57568*n^3+45560*n^2 -8928*n+630)/315: n in [1..30]]; // _Vincenzo Librandi_, Oct 17 2013
%K nonn,easy
%O 0,2
%A mbaake(AT)sunelc3.tphys.physik.uni-tuebingen.de (Michael Baake)
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