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A106835 4 X 4 vector Markov sequence with characteristic polynomial x^4-10*x^3+25*x^2-4. 0
0, 4, 22, 114, 590, 3066, 15998, 83786, 440270, 2320314, 12260382, 64931114, 344562670, 1831630106, 9751275838, 51981730186, 277413656590, 1481919831674, 7922862005342, 42388551182314, 226923616315950, 1215450062928346 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

(x^2-5x+2)(x^2-5x-2), with roots x=(5 +- sqrt(25 +- 8))/2, or {{x -> -0.372281}, {x -> 0.438447}, {x -> 4.56155}, {x -> 5.37228}}

LINKS

Table of n, a(n) for n=1..22.

FORMULA

M = {{0, 0, 0, 2}, {1, 5, 0, 0}, {0, 2, 0, 0}, {0, 0, 1, 5}}; v[n]=M.v[n-1]; a(n) = v[n][[1]]

G.f.: 2*x^2*(-2+9*x+3*x^2)/((2*x^2+5*x-1)*(2*x^2-5*x+1)). a(n)=(-7*A107839(n)+33*A107839(n-1)+A015535(n+1)-3*A015535(n))/4. a(n) = 10*a(n-1)-25*a(n-2)+4*a(n-4). [From R. J. Mathar, Apr 07 2009]

MATHEMATICA

M = {{0, 0, 0, 2}, {1, 5, 0, 0}, {0, 2, 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}]

CROSSREFS

Sequence in context: A274799 A290591 A272435 * A293966 A305554 A291183

Adjacent sequences:  A106832 A106833 A106834 * A106836 A106837 A106838

KEYWORD

nonn

AUTHOR

Roger L. Bagula, May 30 2005

EXTENSIONS

Edited by Associate Editors of the OEIS, Apr 05 2009

STATUS

approved

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Last modified June 25 12:55 EDT 2019. Contains 324352 sequences. (Running on oeis4.)