OFFSET
0,2
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,0,-1).
FORMULA
G.f.: x*(3-2*x) / (x^3-2*x+1).
a(n) = 2*a(n-1) - a(n-3) for n>=3. - Ron Knott, Aug 25 2006
a(n) = 4*F(n) + F(n-1) - 1, where F = A000045. - Bruno Berselli, Feb 20 2017
a(n) = (-10 + (5-7*sqrt(5))*((1-sqrt(5))/2)^n + ((1+sqrt(5))/2)^n*(5+7*sqrt(5))) / 10. - Colin Barker, Feb 20 2017
MAPLE
with(combinat): seq(fibonacci(n)+fibonacci(n+5)-1, n=-2..30); # Zerinvary Lajos, Feb 01 2008
MATHEMATICA
Table[(3 LucasL[n] - Fibonacci[n] - 2)/2, {n, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 02 2012 *)
LinearRecurrence[{2, 0, -1}, {0, 3, 4}, 40] (* Vladimir Joseph Stephan Orlovsky, Feb 02 2012 *)
CoefficientList[Series[x (3 - 2 x)/(x^3 - 2 x + 1), {x, 0, 20}], x] (* Eric W. Weisstein, Mar 26 2018 *)
PROG
(PARI) concat(0, Vec(x*(3-2*x)/(x^3-2*x+1) + O(x^50))) \\ Colin Barker, Feb 20 2017
(PARI) a(n) = if(n==0, 0, if(n==1, 3, a(n-1)+a(n-2)+1)) \\ Felix Fröhlich, Mar 26 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved