OFFSET
0,4
COMMENTS
Lim_{n->infinity} a(n)/a(n-1) = 1.70490277..., the real root of x^5 = x^4 + x^3 + 1.
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
Peter Borwein and Kevin G. Hare, Some computations on Pisot and Salem numbers, 2000, table 1, p. 7.
Peter Borwein and Kevin G. Hare, Some computations on the spectra of Pisot and Salem numbers, Math. Comp. 71 (2002), 767-780.
Index entries for linear recurrences with constant coefficients, signature (1,0,1,1,1,0,1).
FORMULA
G.f.: x*(1 + x^2 - x^5) / ((1 + x^2)*(1 - x - x^2 - x^5)). - Colin Barker, Dec 17 2017
MATHEMATICA
LinearRecurrence[{1, 0, 1, 1, 1, 0, 1}, {0, 1, 1, 2, 3, 5, 8}, 50] (* Harvey P. Dale, May 21 2012 *)
PROG
(PARI) concat([0], Vec(x*(1 + x^2 - x^5) / ((1 + x^2)*(1 - x - x^2 - x^5)) + O(x^40))) \\ Colin Barker, Dec 17 2017
(Magma) m:=40; R<x>:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!(x*(1 +x^2-x^5)/((1+x^2)*(1-x-x^2-x^5)))); // G. C. Greubel, Nov 03 2018
CROSSREFS
KEYWORD
nonn,easy,less
AUTHOR
Roger L. Bagula, May 27 2005
EXTENSIONS
Entry rewritten by Charles R Greathouse IV, Jan 26 2011
STATUS
approved