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Search: id:A107387
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| A107387 |
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A quartic Fibonacci type alternating / chaotic vector Markov sequence of a quartic characteristic: x^4+3*x^2-3*x-1 for m=3. |
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+0
2
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| 0, 1, 1, 2, 3, 13, 32, 89, 231, 610, 1595, 4181, 10944, 28657, 75023, 196418, 514227, 1346269, 3524576, 9227465, 24157815, 63245986, 165580139, 433494437, 1134903168, 2971215073, 7778742047, 20365011074, 53316291171, 139583862445, 365435296160, 956722026041, 2504730781959, 6557470319842, 17167680177563, 44945570212853, 117669030460992, 308061521170129, 806515533049391, 2111485077978050, 5527939700884755, 14472334024676221, 37889062373143904, 99194853094755497, 259695496911122583, 679891637638612258, 1779979416004714187, 4660046610375530309, 12200160415121876736, 31940434634990099905
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Phi squared real roots: {{x -> -2.61803}, {x -> -1.}, {x -> -0.381966}, {x -> 1.}}
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FORMULA
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m=3; M = {{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, m, 0, -m}}; v[n] = M.v[n - 1]; a(n) =Abs[v[n][[1]]].
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MATHEMATICA
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Clear[M, m, v, aa] (*A107387*)m = 3; 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; aa = Table[Abs[v[n][[1]]], {n, 1, digits}]
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CROSSREFS
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Sequence in context: A072997 A037428 A073688 this_sequence A151461 A082539 A100424
Adjacent sequences: A107384 A107385 A107386 this_sequence A107388 A107389 A107390
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KEYWORD
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nonn,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), May 24 2005, corrected Sep 04 2008
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