OFFSET
0,2
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
T. D. Noe, Table of n, a(n) for n = 0..500
Massimiliano Fasi and Gian Maria Negri Porzio, Determinants of Normalized Bohemian Upper Hessemberg Matrices, University of Manchester (England, 2019).
Martin Griffiths, On a Matrix Arising from a Family of Iterated Self-Compositions, Journal of Integer Sequences, 18 (2015), #15.11.8.
J. A. H. Hunter and F. D. Parker, Problem B-100, Fib. Quart., 5 (1967), p. 288.
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
Index entries for linear recurrences with constant coefficients, signature (2,0,-1).
FORMULA
From Henry Bottomley, Feb 20 2001: (Start)
G.f.: (1+x-3x^2)/(1-2*x+x^3). (End)
If n>=4, a(n) = floor(Phi*a(n-1)); Phi = (1 + sqrt(5))/2. - Philippe Deléham, Aug 08 2003
a(n) = F(n-2) + F(n+1) + 1, n >= 0 (where F(n) is the n-th Fibonacci number). - Zerinvary Lajos, Feb 01 2008
MAPLE
A001588:=-(-1-z+3*z**2)/(z-1)/(z**2+z-1); # conjectured by Simon Plouffe in his 1992 dissertation
with(combinat): seq(fibonacci(n-2) + fibonacci(n+1) + 1, n = 0..35); # Zerinvary Lajos, Feb 01 2008
MATHEMATICA
Fibonacci[Range[0, 100]]*2+1 (* Vladimir Joseph Stephan Orlovsky, Mar 19 2010 *)
PROG
(PARI) a(n)=2*fibonacci(n)+1 \\ Charles R Greathouse IV, Apr 06 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved