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A107378
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Expansion of x*(1-3*x-2*x^2)/(1-4*x+4*x^3+x^4).
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1
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0, 1, 1, 2, 4, 11, 35, 122, 440, 1609, 5913, 21770, 80204, 295555, 1089227, 4014322, 14794864, 54526993, 200961457, 740652050, 2729705364, 10060448635, 37078224883, 136653426026, 503642204200, 1856195468633, 6841089945545
(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 characteristic polynomial x^4-4*x^3+4*x+1.
Setting m=3 gives a Fibonacci sequence.
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MATHEMATICA
| m = 4 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. A107377.
Sequence in context: A126149 A000088 A071794 * A186998 A193058 A179379
Adjacent sequences: A107375 A107376 A107377 * A107379 A107380 A107381
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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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