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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 Table of n, a(n) for n=0..27. 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 Sequence in context: A061285 A194810 A271216 * A372256 A165904 A192008 Adjacent sequences: A101997 A101998 A101999 * A102001 A102002 A102003 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.)