OFFSET
0,2
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
Diana Savin and Elif Tan, On Companion sequences associated with Leonardo quaternions: Applications over finite fields, arXiv:2403.01592 [math.CO], 2024. See p. 2.
Index entries for linear recurrences with constant coefficients, signature (2,0,-1).
FORMULA
a(n) = Fibonacci(n-2) + Fibonacci(n+4) - 1. - Zerinvary Lajos, Feb 01 2008
From R. J. Mathar, Apr 07 2011: (Start)
G.f.: (1 + 3*x - 3*x^2) / ((1-x)*(1 - x - x^2)).
a(n) = A022112(n) - 1. (End)
MAPLE
with(combinat): seq(fibonacci(n-2)+fibonacci(n+4)-1, n=0..29); # Zerinvary Lajos, Feb 01 2008
MATHEMATICA
LinearRecurrence[{2, 0, -1}, {1, 5, 7}, 40] (* Harvey P. Dale, Nov 19 2014 *)
PROG
(Haskell)
a022319 n = a022319_list !! (n-1)
a022319_list = 1 : 5 : zipWith (+)
(map (+ 1) a022319_list) (tail a022319_list)
-- Reinhard Zumkeller, May 26 2013
(PARI) x='x+O('x^50); Vec((1 +3*x -3*x^2)/((1-x)*(1 -x -x^2))) \\ G. C. Greubel, Aug 25 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved