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A122577
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2 X 2 vector matrix Markov as 4 switched vector states modulo 4 with two Fibonacci-like matrix states and one flipping matrix modulo 3.
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0
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1, 1, 7, 10, 1, 169, 21, 2, 1801, 144, 1, 39202, 521, 1, 275807, 3194, 1, 6625109, 6765, 2, 70602821, 46368, 1, 1536796802, 167761, 1, 10812186007, 1028458, 1, 259717522849, 2178309, 2, 2767771787041, 14930352, 1, 60245508192802
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Adding the flipping matrix that is out of synchronization with the input vector states produces a chaotic effect. The model is based on a BCS superconductor state model that is switched between an Heissenberg spin model and an Ising magnetization model as a sequential heat bath.
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REFERENCES
| R. Brout,Phase Transitions,Low Temperature Physics LT9, PartB,Plenum Press, New York,1965, p 623-636
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FORMULA
| a[1] = {2, 2}; a[2] = {2, 1}; a[3] = {1, 2}; a[4] = {1, 1}; M[n_] := If[Mod[n, 3] == 0, {{ 0, 1}, {1, 2}}, If[Mod[n, 3] == 1, {{0, 1}, {1, 1}}, {{0, 1}, {1, 0}}]] v[n_] := v[n] = MatrixPower[M[n], n].a[1 + Mod[n, 4]] a(n) = v[n][[1]]
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MATHEMATICA
| a[1] = {2, 2}; a[2] = {2, 1}; a[3] = {1, 2}; a[4] = {1, 1}; M[n_] := If[Mod[n, 3] == 0, {{ 0, 1}, {1, 2}}, If[Mod[n, 3] == 1, {{0, 1}, {1, 1}}, {{0, 1}, {1, 0}}]] v[n_] := v[n] = MatrixPower[M[n], n].a[1 + Mod[n, 4]] a1 = Table[v[n][[1]], {n, 1, 50}]
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CROSSREFS
| Sequence in context: A027723 A046265 A082705 * A180732 A070405 A010730
Adjacent sequences: A122574 A122575 A122576 * A122578 A122579 A122580
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KEYWORD
| nonn,uned
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AUTHOR
| Roger Bagula (rlbagulatftn(AT)yahoo.com), Sep 17 2006
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