OFFSET
0,1
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,-5,1).
FORMULA
G.f.: (2x-1)(x-3)/((1-x)(x^2-4x+1)).
a(0)=3, a(1)=8, a(2)=27, a(n) = 5*a(n-1) - 5*a(n-2) + a(n-3). - Harvey P. Dale, Jul 25 2012
a(n) = (2+(2-sqrt(3))^(1+n)+(2+sqrt(3))^(1+n))/2. - Colin Barker, Nov 03 2016
MATHEMATICA
a[0] = 3; a[1] = 8; a[n_] := a[n] = 4a[n - 1] - a[n - 2] - 2; Table[a[n], {n, 0, 23}] (* Or *)
CoefficientList[ Series[(2x - 1)(x - 3)/((1 - x)(x^2 - 4x + 1)), {x, 0, 22}], x] (* Robert G. Wilson v, Jan 12 2005 *)
LinearRecurrence[{5, -5, 1}, {3, 8, 27}, 30] (* Harvey P. Dale, Jul 25 2012 *)
PROG
(PARI) Vec((2*x-1)*(x-3)/((1-x)*(x^2-4*x+1)) + O(x^30)) \\ Colin Barker, Nov 03 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Creighton Dement, Dec 30 2004
EXTENSIONS
More terms from Robert G. Wilson v, Jan 12 2005
Recurrence in the definition corrected by R. J. Mathar, Aug 07 2008
STATUS
approved