A022154 - OEIS

%I #33 Mar 15 2024 10:59:05

%S 1,288,15776,346304,4254912,34792672,210482016,1010803584,4047994752,

%T 14009305760,43023042336,119628650560,305908697152,728298521184,

%U 1630273964256,3458692036352,7000203482880,13590066551840,25423081113760,46005461684160,80797523590080

%N Coordination sequence for root lattice B_12.

%H Vincenzo Librandi, <a href="/A022154/b022154.txt">Table of n, a(n) for n = 0..1000</a>

%H M. Baake and U. Grimm, <a href="https://arxiv.org/abs/cond-mat/9706122">Coordination sequences for root lattices and related graphs</a>, arXiv:cond-mat/9706122, 1997; Zeit. f. Kristallographie, 212 (1997), 253-256

%H R. Bacher, P. de la Harpe and B. Venkov, <a href="http://dx.doi.org/10.1016/S0764-4442(97)83542-2">Séries de croissance et séries d'Ehrhart associées aux réseaux de racines</a>, C. R. Acad. Sci. Paris, 325 (Series 1) (1997), 1137-1142.

%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).

%F 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

%F 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

%t 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 *)

%o (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

%K nonn,easy

%O 0,2

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