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A094726
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Let M = the 2 X 2 matrix [ 0 3 / 3 2]. Take (M^n * [1 1])/3 = [p q]; then a(n) = p.
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0
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1, 5, 19, 83, 337, 1421, 5875, 24539, 101953, 424757, 1767091, 7356995, 30617809, 127448573, 530457427, 2207952011, 9190020865, 38251609829, 159213407443, 662691303347, 2758303273681, 11480828277485, 47786386018099
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = 2*a(n-1)+9*a(n-2).
G.f.: -x*(3*x+1)/(9*x^2+2*x-1). (End)
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EXAMPLE
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a(6) = 1421 since (M^n * [1 1])/3 = [1421 q].
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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