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A107377
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Expansion of x*(1-4*x-3*x^2)/(1-5*x+5*x^3+x^4).
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1
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0, 1, 1, 2, 5, 19, 84, 393, 1865, 8886, 42381, 202187, 964640, 4602409, 21958729, 104768258, 499864605, 2384926971, 11378834836, 54290082897, 259025915025, 1235850473974, 5896423120549, 28132695944723, 134225201438720
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Sequence produced by 4 X 4 Markov chain with symmetric quartic characteristic polynomial x^4-5*x^3+5*x+1.
Setting m=3 gives a Fibonacci sequence.
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FORMULA
| Let m=5, M={{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {-1, -m, 0, m}}, v[n]=M.v[n-1], then a(n) = v[n][[1]].
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MATHEMATICA
| m = 5 M = {{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {-1, -m, 0, m}} Expand[Det[M - x*IdentityMatrix[4]]] NSolve[Det[M - x*IdentityMatrix[4]] == 0, x] 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
| Cf. A107378.
Sequence in context: A138911 A181513 A179566 * A058132 A002851 A124348
Adjacent sequences: A107374 A107375 A107376 * A107378 A107379 A107380
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KEYWORD
| nonn
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), May 24 2005
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Jul 13 2007
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