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A022148 Coordination sequence for root lattice B_6.

%I A022148 #23 Aug 11 2025 15:13:51
%S A022148 1,72,1072,6968,28320,85992,214864,467544,918080,1665672,2838384,
%T A022148 4596856,7138016,10698792,15559824,22049176,30546048,41484488,
%U A022148 55357104,72718776,94190368,120462440,152298960
%N A022148 Coordination sequence for root lattice B_6.
%H A022148 Vincenzo Librandi, <a href="/A022148/b022148.txt">Table of n, a(n) for n = 0..1000</a>
%H A022148 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, Zeit. f. Kristallographie, 212 (1997), 253-256.
%H A022148 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 A022148 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A022148 a(0) = 1; for n>0, a(n) = (8*n/15)*(58*n^4 - 65*n^3 + 180*n^2 - 85*n + 47) . - _Philippe Deléham_, Feb 20 2004
%F A022148 G.f.: (1+66*x+655*x^2+1596*x^3+1167*x^4+226*x^5+x^6)/(1-x)^6 = 1+8*x*(9+80*x+202*x^2+144*x^3+29*x^4)/(1-x)^6. - _Colin Barker_, Apr 13 2012
%t A022148 CoefficientList[Series[(1+66*x+655*x^2+1596*x^3+1167*x^4+ 226*x^5+x^6)/(1-x)^6,{x,0,40}],x] (* _Vincenzo Librandi_, Apr 20 2012 *)
%t A022148 LinearRecurrence[{6,-15,20,-15,6,-1},{1,72,1072,6968,28320,85992,214864},30] (* _Harvey P. Dale_, Aug 11 2025 *)
%o A022148 (Magma) [1] cat[(8*n/15)*(58*n^4 - 65*n^3 + 180*n^2 - 85*n + 47) : n in [1..40]]; // _Vincenzo Librandi_, Apr 20 2012
%K A022148 nonn,easy
%O A022148 0,2
%A A022148 mbaake(AT)sunelc3.tphys.physik.uni-tuebingen.de (Michael Baake)