OFFSET
0,2
COMMENTS
Based on taking the n-th power of the matrix M = [1 1 1 1 / 2 0 0 0 / 0 2 0 0 / 0 0 2 0] that generates the D_4 lattice.
a(n)/a(n-1) tends to 2.698068913... an eigenvalue of M and a root of the characteristic polynomial x^4 - x^3 - 2*x^2 - 4*x - 8.
LINKS
J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, Springer-Verlag, 3rd edition, 1999. (See Chap. 4.)
Index entries for linear recurrences with constant coefficients, signature (1,2,4,8).
FORMULA
G.f.: (-1-x+4*x^3)/(-1+x+2*x^2+4*x^3+8*x^4). [R. J. Mathar, Feb 13 2010]
MATHEMATICA
LinearRecurrence[{1, 2, 4, 8}, {1, 2, 4, 8}, 28] (* Hugo Pfoertner, Dec 11 2022 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Dec 23 2004
EXTENSIONS
More terms from R. J. Mathar, Feb 13 2010
Edited by N. J. A. Sloane, Dec 11 2022
STATUS
approved