OFFSET
0,3
LINKS
David Garth and Kevin G. Hare, Comments on the spectra of Pisot numbers, J. Number Theory 121 (2006), 187-203.
Index entries for linear recurrences with constant coefficients, signature (2, 1, 1).
FORMULA
lim_{n-> infinity} a(n)/a(n-1)= 2.54682...
G.f.: (1-x-x^2)/(1-2*x-x^2-x^3). [Sep 28 2009]
MATHEMATICA
a = 2; b = -1; M = {{0, 1, 0, 0, 0}, { a - 2, a - 2, a - 2 - b, a - 2 - b, 0}, {1, 1, 1, 1, 0}, {0, 1, 1, 0, 0}, {0, 0, 0, 1, 1}} v[1] = {1, 1, 1, 1, 1} v[n_] := v[n] = M.v[n - 1] a0 = Table[Abs[v[n][[1]]], {n, 1, 50}]
LinearRecurrence[{2, 1, 1}, {1, 1, 2}, 30] (* Harvey P. Dale, Aug 05 2015 *)
Lucas := 1 + x (1 + 2 x)/(1 - x - x^2); (* InvertTransform defined in A052987 *)
InvertTransform[Lucas, 28] (* Peter Luschny, Jan 10 2019 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula, Jun 20 2005
EXTENSIONS
Definition replaced by recurrence by the Associate Editors of the OEIS, Sep 28 2009
STATUS
approved