A022153 Coordination sequence for root lattice B_11.

1, 242, 11242, 210474, 2224178, 15804866, 83999962, 358159802, 1285951458, 4025098770, 11267030346, 28752157898, 67886298898, 150029971938, 313233102138, 622431249242, 1184409984450, 2169185665330, 3839847763114, 6593364255082, 11015371578354, 17952558422018

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

M. Baake and U. Grimm, Coordination sequences for root lattices and related graphs, arXiv:cond-mat/9706122, 1997; Zeit. f. Kristallographie, 212 (1997), 253-256.

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.

Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Formula

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

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

Mathematica

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 *)

Prog

(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

Crossrefs

Sequence in context: A006601 A283723 A035748 * A335611 A194788 A338454

Adjacent sequences: A022150 A022151 A022152 * A022154 A022155 A022156

Keyword

nonn,easy

Author

mbaake(AT)sunelc3.tphys.physik.uni-tuebingen.de (Michael Baake)

Status

approved