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Coordination sequence for root lattice B_11.
4

%I #27 Mar 15 2024 11:16:52

%S 1,242,11242,210474,2224178,15804866,83999962,358159802,1285951458,

%T 4025098770,11267030346,28752157898,67886298898,150029971938,

%U 313233102138,622431249242,1184409984450,2169185665330,3839847763114,6593364255082,11015371578354,17952558422018

%N Coordination sequence for root lattice B_11.

%H Vincenzo Librandi, <a href="/A022153/b022153.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, 1997; 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_11">Index entries for linear recurrences with constant coefficients</a>, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

%F a(0)=1; for n>0, a(n) = ( 16296*n^10 - 40520*n^9 + 422820*n^8 - 772320*n^7 + 3019968*n^6 - 3688440*n^5 + 6425580*n^4 - 4306480*n^3 + 2872836*n^2 - 547740*n + 28350 ) / 14175. - _Ralf Stephan_, Apr 28 2004

%F G.f.: -(x^11 +1551*x^10 +32659*x^9 +242517*x^8 +812570*x^7 +1346534*x^6 +1139446*x^5 +487674*x^4 +99957*x^3 +8635*x^2 +231*x +1) / (x -1)^11. - _Colin Barker_, Nov 18 2012

%t CoefficientList[Series[-(x^11 + 1551 x^10 + 32659 x^9 + 242517 x^8 + 812570 x^7 + 1346534 x^6+1139446 x^5 + 487674 x^4 + 99957 x^3 + 8635 x^2 + 231 x + 1)/(x - 1)^11, {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 17 2013 *)

%o (Magma) [1] cat [(16296*n^10 -40520*n^9 +422820*n^8 -772320*n^7 +3019968*n^6 -3688440*n^5 +6425580*n^4 -4306480*n^3 +2872836*n^2 -547740*n +28350)/14175: 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)