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A008376 Coordination sequence for D_9 lattice.

%I A008376 #27 Sep 06 2023 01:42:26
%S A008376 1,144,4194,50832,361602,1801872,6976866,22413456,62407170,155242640,
%T A008376 352624482,743284368,1471858818,2764261008,4960898658,8559218832,
%U A008376 14267189250,23069454480,36308034146,55779559056,83851169922,123597332112,178959948642,254934282384,357783327234
%N A008376 Coordination sequence for D_9 lattice.
%H A008376 Vincenzo Librandi, <a href="/A008376/b008376.txt">Table of n, a(n) for n = 0..1000</a>
%H A008376 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 A008376 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 A008376 <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 A008376 G.f.: -(x +1)*(x^8 +134*x^7 +2800*x^6 +15386*x^5 +27742*x^4 +15386*x^3 +2800*x^2 +134*x +1) / (x -1)^9. [_Colin Barker_, Nov 18 2012]
%p A008376 1006/315*n^8+488/15*n^6+1084/15*n^4+10712/315*n^2+2;
%t A008376 CoefficientList[Series[-(x + 1) (x^8 + 134 x^7 + 2800 x^6 + 15386 x^5 + 27742 x^4 + 15386 x^3 + 2800 x^2 + 134 x + 1)/(x - 1)^9, {x, 0, 40}], x] (* _Vincenzo Librandi_, Oct 15 2013 *)
%t A008376 LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{1,144,4194,50832,361602,1801872,6976866,22413456,62407170,155242640},30] (* _Harvey P. Dale_, Jun 05 2023 *)
%Y A008376 A row of array A103903.
%K A008376 nonn,easy
%O A008376 0,2
%A A008376 _N. J. A. Sloane_ and _J. H. Conway_
%E A008376 More terms from _Vincenzo Librandi_, Oct 15 2013