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
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).
Programs
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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
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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 *)
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