A022154 Coordination sequence for root lattice B_12.

1, 288, 15776, 346304, 4254912, 34792672, 210482016, 1010803584, 4047994752, 14009305760, 43023042336, 119628650560, 305908697152, 728298521184, 1630273964256, 3458692036352, 7000203482880, 13590066551840, 25423081113760, 46005461684160, 80797523590080

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 (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).

Formula

a(0)=1; for n>0, a(n) = ( 65344*n^11 - 179168*n^10 + 2231680*n^9 - 4643760*n^8 + 22442112*n^7 - 33057024*n^6 + 76060160*n^5 - 69575440*n^4 + 72405344*n^3 - 29758608*n^2 + 8915760*n ) / 155925. - Ralf Stephan, Apr 28 2004

G.f.: (x^12 +2036*x^11 +51810*x^10 +476740*x^9 +2035055*x^8 +4446312*x^7 +5189212*x^6 +3260840*x^5 +1077615*x^4 +175780*x^3 +12386*x^2 +276*x +1) / (x -1)^12. - Colin Barker, Nov 18 2012

Mathematica

CoefficientList[Series[(x^12 + 2036 x^11 + 51810 x^10 + 476740 x^9 + 2035055 x^8 + 4446312 x^7 + 5189212 x^6 + 3260840 x^5 + 1077615 x^4 + 175780 x^3 + 12386 x^2 + 276 x + 1)/(x - 1)^12, {x, 0, 30}], x] (* Vincenzo Librandi, Oct 17 2013 *)

Prog

(Magma) [1] cat [(65344*n^11-179168*n^10+2231680*n^9-4643760*n^8+22442112*n^7-33057024*n^6 +76060160*n^5-69575440*n^4+72405344*n^3-29758608*n^2+8915760*n)/155925: n in [1..30]]; // Vincenzo Librandi, Oct 17 2013

Crossrefs

Sequence in context: A223293 A035749 A048145 * A285923 A285859 A163007

Adjacent sequences: A022151 A022152 A022153 * A022155 A022156 A022157

Keyword

nonn,easy

Author

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

Status

approved