A102206 a(0) = 3, a(1) = 8, a(n+2) = 4*a(n+1) - a(n) - 2.

3, 8, 27, 98, 363, 1352, 5043, 18818, 70227, 262088, 978123, 3650402, 13623483, 50843528, 189750627, 708158978, 2642885283, 9863382152, 36810643323, 137379191138, 512706121227, 1913445293768, 7141075053843, 26650854921602, 99462344632563, 371198523608648

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(n) = A092184(n+1) + 2; a(n+1) - a(n) = A001834(n+1) (see comment).

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

Cf. A092184, A001834, A001353, A102207.

Sequence in context: A148844 A145760 A102318 * A192856 A110886 A104854

Adjacent sequences: A102203 A102204 A102205 * A102207 A102208 A102209

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