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Coordination sequence for 8-dimensional cyclotomic lattice Z[zeta_24].
0

%I #11 Jun 13 2015 00:52:18

%S 1,24,264,1800,8736,32952,102744,276648,663744,1451736,2944104,

%T 5607624,10131552,17499768,29077176,46711656,72852864,110689176,

%U 164304072,238853256,340763808,477956664,660093720,898850856,1208218176,1604828760,2108317224

%N Coordination sequence for 8-dimensional cyclotomic lattice Z[zeta_24].

%H M. Beck and S. Hosten, <a href="http://arxiv.org/abs/math/0508136">Cyclotomic polytopes and growth series of cyclotomic lattices</a>, arXiv math.CO/0508136

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8, -28, 56, -70, 56, -28, 8, -1).

%F G.f.: (x^2+4*x+1)^4/(1-x)^8.

%F a(0)=1, a(1)=24, a(2)=264, a(3)=1800, a(4)=8736, a(5)=32952, a(6)=102744, a(7)=276648, a(8)=663744, a(n)=8*a(n-1)-28*a(n-2)+56*a(n-3)- 70*a(n-4)+ 56*a(n-5)-28*a(n-6)+8*a(n-7)-a(n-8) [From Harvey P. Dale, Apr 09 2012]

%t CoefficientList[Series[(x^2+4x+1)^4/(1-x)^8,{x,0,30}],x] (* or *) Join[{1},LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{24,264,1800,8736,32952,102744,276648,663744},30]] (* _Harvey P. Dale_, Apr 09 2012 *)

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Mar 18 2007