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

Author

Creighton Dement, Dec 30 2004

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-5,1).

Crossrefs

Cf. A092184, A001834, A001353, A102207.

Programs

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 *)

PARI

Vec((2*x-1)*(x-3)/((1-x)*(x^2-4*x+1)) + O(x^30)) \\ Colin Barker, Nov 03 2016

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

Extensions

More terms from Robert G. Wilson v, Jan 12 2005

Recurrence in the definition corrected by R. J. Mathar, Aug 07 2008