OFFSET
0,1
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (-2,2,1).
FORMULA
a(n) = 2+(-1)^n*L(2n).
a(n) = -2a(n-1)+2a(n-2)+a(n-3) with a(0)=4, a(1)=-1, a(2)=9.
G.f.: (4 + 7*x - x^2)/(1 + 2*x - 2*x^2 - x^3).
a(n) = (-1)^n*A001254(n). - R. J. Mathar, Jan 11 2012
a(n) = (2+(1/2*(-3-sqrt(5)))^n+(1/2*(-3+sqrt(5)))^n). - Colin Barker, Oct 01 2016
MATHEMATICA
CoefficientList[Series[(4 + 7*x - x^2)/(1 + 2*x - 2*x^2 - x^3), {x, 0, 30}], x]
LinearRecurrence[{-2, 2, 1}, {4, -1, 9}, 50] (* Harvey P. Dale, Nov 08 2011 *)
PROG
(PARI) a(n) = round((2+(1/2*(-3-sqrt(5)))^n+(1/2*(-3+sqrt(5)))^n)) \\ Colin Barker, Oct 01 2016
(PARI) Vec((4+7*x-x^2)/(1+2*x-2*x^2-x^3) + O(x^30)) \\ Colin Barker, Oct 01 2016
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Mario Catalani (mario.catalani(AT)unito.it), Sep 05 2002
STATUS
approved