A126904 Coordination sequence for 8-dimensional cyclotomic lattice Z[zeta_24].

1, 24, 264, 1800, 8736, 32952, 102744, 276648, 663744, 1451736, 2944104, 5607624, 10131552, 17499768, 29077176, 46711656, 72852864, 110689176, 164304072, 238853256, 340763808, 477956664, 660093720, 898850856, 1208218176, 1604828760, 2108317224

Offset

0,2

Links

Table of n, a(n) for n=0..26.

M. Beck and S. Hosten, Cyclotomic polytopes and growth series of cyclotomic lattices, arXiv math.CO/0508136

Index entries for linear recurrences with constant coefficients, signature (8, -28, 56, -70, 56, -28, 8, -1).

Formula

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

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]

Mathematica

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 *)

Crossrefs

Sequence in context: A187380 A000145 A286346 * A001413 A022065 A125412

Adjacent sequences: A126901 A126902 A126903 * A126905 A126906 A126907

Keyword

nonn

Author

N. J. A. Sloane, Mar 18 2007

Status

approved