A022151 Coordination sequence for root lattice B_9.

1, 162, 5154, 67266, 507906, 2653346, 10666146, 35310402, 100746498, 255708578, 590675490, 1262903490, 2531446530, 4804547490, 8702041250, 15135668034, 25410452994, 41350565538, 65453329442, 101075312322, 152654680578, 225974263458, 328470027426, 469589919554

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, 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 (9,-36,84,-126,126,-84,36,-9,1).

Formula

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

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

Mathematica

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 *)
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 *)

Prog

(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

Crossrefs

Sequence in context: A128803 A035746 A285046 * A279917 A291131 A209965

Adjacent sequences: A022148 A022149 A022150 * A022152 A022153 A022154

Keyword

nonn,easy

Author

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

Status

approved