A116560 Sequentially switched Markov of six 2 X 2 matrices based on the Anharmonic group that gives a chaotic vector output.

0, 1, 1, 0, 0, 1, 1, 1, 2, 1, 1, 2, 2, 3, 5, 2, 2, 5, 5, 7, 12, 5, 5, 12, 12, 17, 29, 12, 12, 29, 29, 41, 70, 29, 29, 70, 70, 99, 169, 70, 70, 169, 169, 239, 408, 169, 169, 408, 408, 577, 985, 408, 408, 985, 985, 1393, 2378, 985, 985, 2378, 2378

Offset

0,9

Comments

This group is isomorphic (can be mapped to) with the SL[2,2] as a representation of S3, even permutation group. Second element is alternating here and gives a cycle with the first: b = Table[v[n][[2]], {n, 0, 36}] {1, 1, 1, 1, -1, -1, -1, -2, -1, -2, 3, 3, 3, 5, 3, 5, -7, -7, -7, -12, -7, -12, 17, 17, 17, 29, 17, 29, -41, -41, -41, -70, -41, -70, 99, 99, 99}.

References

Blyth and Robonson, Essential Student Algebra, V5, Groups, J. W. Arrowsmith, Bristol, 1986, page 9.

McKean and Moll, Elliptic Curves, Cambridge, New York, 1997, pages 13, 169-171.

Andree, Selections from Modern Algebra, Henry Holt and Co, New York, 1958, pages 86, 91.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

From R. J. Mathar, Nov 28 2008: (Start)

a(n) = 2*a(n-6) + a(n-12).

G.f.: x*(1+x+x^4+x^5-x^6+x^8+x^9)/(1-2*x^6-x^12).

a(6*n) = a(6*n+3) = a(6*n+4) = A000129(n).

a(6*n+1) = A001333(n).

a(6*n+2) = a(6*n+5) = A000129(n+1). (End)

Mathematica

CoefficientList[Series[x*(1 + x + x^4 + x^5 - x^6 + x^8 + x^9)/(1 - 2 x^6 - x^12), {x, 0, 50}], x] (* G. C. Greubel, Sep 20 2017 *)

Prog

(PARI) x='x+O('x^50); Vec(x*(1+x+x^4+x^5-x^6+x^8+x^9)/(1-2*x^6-x^12)) \\ G. C. Greubel, Sep 20 2017

Crossrefs

Sequence in context: A234716 A357383 A181885 * A309224 A103784 A153916

Adjacent sequences: A116557 A116558 A116559 * A116561 A116562 A116563

Keyword

nonn,obsc

Author

Roger L. Bagula, Mar 17 2006

Extensions

Terms a(37) onward added by G. C. Greubel, Sep 20 2017

Status

approved