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A022154
Coordination sequence for root lattice B_12.
4
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
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
KEYWORD
nonn,easy
AUTHOR
mbaake(AT)sunelc3.tphys.physik.uni-tuebingen.de (Michael Baake)
STATUS
approved