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A122577 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. 0
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; text; internal format)
OFFSET

1,3

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 Heisenberg spin model and an Ising magnetization model as a sequential heat bath.

REFERENCES

R. Brout,Phase Transitions,Low Temperature Physics LT9, PartB,Plenum Press, New York,1965, p 623-636

LINKS

Table of n, a(n) for n=1..36.

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}]

CROSSREFS

Sequence in context: A027723 A046265 A082705 * A180732 A266551 A070405

Adjacent sequences:  A122574 A122575 A122576 * A122578 A122579 A122580

KEYWORD

nonn,uned

AUTHOR

Roger L. Bagula, Sep 17 2006

STATUS

approved

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Last modified October 17 21:16 EDT 2019. Contains 328132 sequences. (Running on oeis4.)