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

%I A094726 #14 Jan 06 2025 01:21:53
%S A094726 1,5,19,83,337,1421,5875,24539,101953,424757,1767091,7356995,30617809,
%T A094726 127448573,530457427,2207952011,9190020865,38251609829,159213407443,
%U A094726 662691303347,2758303273681,11480828277485,47786386018099
%N A094726 Let M = the 2 X 2 matrix [ 0 3 / 3 2]. Take (M^n * [1 1])/3 = [p q]; then a(n) = p.
%H A094726 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,9).
%F A094726 From _Colin Barker_, Nov 08 2012: (Start)
%F A094726 a(n) = 2*a(n-1)+9*a(n-2).
%F A094726 G.f.: -x*(3*x+1)/(9*x^2+2*x-1). (End)
%e A094726 a(6) = 1421 since (M^n * [1 1])/3 = [1421 q].
%t A094726 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 *)
%Y A094726 Cf. A002534.
%K A094726 nonn,easy
%O A094726 1,2
%A A094726 _Gary W. Adamson_, May 23 2004
%E A094726 Edited, corrected and extended by _Robert G. Wilson v_, Jun 05 2004