A094726 Let M = the 2 X 2 matrix [ 0 3 / 3 2]. Take (M^n * [1 1])/3 = [p q]; then a(n) = p.

1, 5, 19, 83, 337, 1421, 5875, 24539, 101953, 424757, 1767091, 7356995, 30617809, 127448573, 530457427, 2207952011, 9190020865, 38251609829, 159213407443, 662691303347, 2758303273681, 11480828277485, 47786386018099

Offset: 1

Author

Gary W. Adamson, May 23 2004

Keywords

• nonn
• easy

Examples

			a(6) = 1421 since (M^n * [1 1])/3 = [1421 q].
		

Links

• Index entries for linear recurrences with constant coefficients, signature (2,9).

Crossrefs

Cf. A002534.

Programs

Mathematica

a[n_] := (MatrixPower[{{0, 3}, {3, 2}}, n].{{1}, {1}})[[1, 1]]/3; Table[ a[n], {n, 22}] (* Robert G. Wilson v, Jun 05 2004 *)

Formula

From Colin Barker, Nov 08 2012: (Start)

a(n) = 2*a(n-1)+9*a(n-2).

G.f.: -x*(3*x+1)/(9*x^2+2*x-1). (End)

Extensions

Edited, corrected and extended by Robert G. Wilson v, Jun 05 2004