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A102000 a(0),...,a(3) = 1, 2, 4, 8; thereafter a(n) = a(n-1) + 2*a(n-2) + 4*a(n-3) + 8*a(n-4), n>3. 2
1, 2, 4, 8, 32, 80, 208, 560, 1552, 4144, 11152, 30128, 81424, 219440, 592016, 1597616, 4310800, 11629616, 31377808, 84661168, 228421648, 616292144, 1662802576, 4486362800, 12104509712, 32658782768, 88115674000, 237742180784 (list; graph; refs; listen; history; text; internal format)
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.)
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
Sequence in context: A061285 A194810 A271216 * A372256 A165904 A192008
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

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Last modified June 21 03:10 EDT 2024. Contains 373535 sequences. (Running on oeis4.)