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Search: id:A109531
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| A109531 |
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A switched vector Markov between three matrices with the same characteristic polynomial: x^3-x-1 The first stream of three that results. |
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+0
1
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| 0, 1, 1, 1, 1, 4, 1, 3, 7, 3, 6, 16, 6, 13, 34, 13, 28, 73, 28, 60, 157, 60, 129, 337, 129, 277, 724, 277, 595, 1555, 595, 1278, 3340, 1278, 2745, 7174, 2745, 5896, 15409, 5896, 12664, 33097, 12664, 27201, 71089, 27201, 58425, 152692, 58425, 125491, 327967
(list; graph; listen)
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OFFSET
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0,6
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COMMENT
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CharacteristicPolynomial[M1, x] CharacteristicPolynomial[M2, x] CharacteristicPolynomial[M3, x]
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FORMULA
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M[n] =M1 if Mod[n, 3]=1 M[n] =M2 if Mod[n, 3]=2 M[n] =M3 if Mod[n, 3]=0 v[n]=M[n].v[n-1] a(n) = v[n][[1]]
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MATHEMATICA
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M1 = {{0, 1, 0}, {0, 0, 1}, {1, 1, 0}}; M2 = {{0, 1, 1}, {1, 0, 0}, {0, 1, 0}}; M3 = {{0, 1, 0}, {1, 0, 1}, {1, 0, 0}}; M[n_] = If[Mod[n, 3] == 1, M3, If[Mod[n, 3] == 2, M2, M1]]; v[0] = {0, 1, 1}; v[n_] := v[n] = M[n].v[n - 1] a = Table[v[n][[1]], {n, 0, 100}]
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CROSSREFS
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Cf. A000931.
Sequence in context: A134224 A121441 A074813 this_sequence A073817 A074081 A132703
Adjacent sequences: A109528 A109529 A109530 this_sequence A109532 A109533 A109534
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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), Jun 18 2005
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