OFFSET
0,1
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..199
Index entries for linear recurrences with constant coefficients, signature (0,18,0,-1).
FORMULA
G.f.: (8+9*x+8*x^2-x^3)/(1-18*x^2+x^4).
a(n) = 18*a(n-2) - a(n-4).
a(n) = (-3*(-2-sqrt(5))^(n+1) + 5*(2-sqrt(5))^(n+1) - 3*(-2+sqrt(5))^(n+1) + 5*(2+sqrt(5))^(n+1))/4. - Colin Barker, Mar 27 2016
a(n) = (5 - 3*(-1)^(n+1))*Lucas(3*(n+1))/4. - Ehren Metcalfe, Apr 15 2019
MATHEMATICA
CoefficientList[Series[(8+9*x+8*x^2-x^3)/(1-18*x^2+x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 29 2013 *)
PROG
(PARI) Vec((8+9*x+8*x^2-x^3)/(1-18*x^2+x^4) + O(x^30)) \\ Colin Barker, Mar 27 2016
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (8+9*x+8*x^2-x^3)/(1-18*x^2+x^4) )); // G. C. Greubel, Apr 16 2019
(Sage) ((8+9*x+8*x^2-x^3)/(1-18*x^2+x^4)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Apr 16 2019
CROSSREFS
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Colin Barker, Nov 05 2013
First term 1 removed in b-file, formulas and programs by Georg Fischer, Jul 01 2019
STATUS
approved