OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,0,-1).
FORMULA
From R. J. Mathar, Nov 22 2009: (Start)
a(n)= 2*a(n-1) - a(n-3) = 2*A001911(n).
G.f.: 2*x*(1+x)/((x-1)*(x^2+x-1)). (End)
a(n) = a(n-1) + 2*Fibonacci(n+1), with a(0)=0. - Taras Goy, Mar 24 2019
E.g.f.: 4*exp(x/2)*(5*cosh(sqrt(5)*x/2) + 2*sqrt(5)*sinh(sqrt(5)*x/2))/5 - 4*exp(x). - Stefano Spezia, Oct 14 2022
MATHEMATICA
Fibonacci[Range[3, 4! ]]*2-4 (* Vladimir Joseph Stephan Orlovsky, Mar 19 2010 *)
LinearRecurrence[{2, 0, -1}, {0, 2, 6}, 50] (* G. C. Greubel, Jul 15 2016 *)
PROG
(Magma) I:=[0, 2, 6]; [n le 3 select I[n] else Self(n-1)+Self(n-2)+4: n in [1..40]]; // Vincenzo Librandi, Jul 16 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Geoff Ahiakwo, Nov 19 2009
EXTENSIONS
Definition replaced by recurrence from R. J. Mathar, Nov 23 2009
STATUS
approved