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A106850
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4 X 4 vector Markov sequence with characteristic polynomial: x^4-10*x^3+25*x^2-9.
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0
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0, 6, 33, 174, 915, 4854, 25962, 139836, 757545, 4123236, 22527393, 123451554, 678148620, 3732306474, 20572095777, 113524359906, 627044542215, 3465927182766, 19168307134278, 106056611012784, 587001832650825
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OFFSET
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1,2
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COMMENTS
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(x^2-5x+3)(x^2-5x-3), with roots x=(5 +- sqrt(25 +- 12))/2, or {{x -> -0.541381}, {x -> 0.697224}, {x -> 4.30278}, {x -> 5.54138}}
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LINKS
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Table of n, a(n) for n=1..21.
Index to sequences with linear recurrences with constant coefficients, signature (10,-25,0,9).
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FORMULA
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M = {{0, 0, 0, 3}, {1, 5, 0, 0}, {0, 3, 0, 0}, {0, 0, 1, 5}}; v[n]=M.v[n-1]; a(n) = v[n][[1]].
G.f.: 3*x^2*(2*x^2+9*x-2)/((3*x^2-5*x+1)*(3*x^2+5*x-1)). [Colin Barker, Sep 03 2012]
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MATHEMATICA
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M = {{0, 0, 0, 3}, {1, 5, 0, 0}, {0, 3, 0, 0}, {0, 0, 1, 5}}; v[1] = {0, 1, 1, 2}; v[n_] := v[n] = M.v[n - 1]; digits = 50; a = Table[v[n][[1]], {n, 1, digits}]
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CROSSREFS
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Sequence in context: A086314 A086091 A081893 * A094165 A111994 A092851
Adjacent sequences: A106847 A106848 A106849 * A106851 A106852 A106853
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KEYWORD
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nonn,easy
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AUTHOR
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Roger L. Bagula, May 30 2005
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EXTENSIONS
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Edited by Associate Editors of the OEIS, Apr 06 2009
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STATUS
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approved
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