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A143044 A division-matrix vector Markov: where 8 matrices are projectively divided by a 9th matrix and then iterated in order: ( real part ) Matrices: m0 = Inverse[{{0, I}, {I, 1}}]: 9th; M[0] = {{0, -1}, {-1, -1}}.m0; M[1] = {{1, 0}, {-1, -1}}.m0; M[2] = {{-1, 0}, {-1, -1}}.m0; M[3] = {{0, 1}, {-1, -1}}.m0; M[4] = I*{{0, -1}, {-1, -1}}.m0; M[5] = I*{{1, 0}, {-1, -1}}.m0; M[6] = I*{{-1, 0}, {-1, -1}}.m0; M[7] = I*{{0, 1}, {-1, -1}}.m0. 0
1, 1, -3, 0, 0, 4, 6, 5, 18, -23, -24, 24, 17, 88, -7, 145, 5, -376, 376, -236, 654, -755, 34, 3025, -2992, 2992, -5983, -720, -11279, -18015, 48141, -112, 112, -66268, -95338, -85227, -294862, 389049, 381240, -381240, -302671, -1445240, 69609, -2448591, 110613, 6162200, -6162200, 3602996 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

This set of matrices as Moebius transforms and ratio=1/Sqrt[8]

gives a three part fractal. The object is to simulate

a SU(3) level of orthogonality using a division type set of Determinant and -1

matrices.

LINKS

Table of n, a(n) for n=1..48.

FORMULA

Matrices: m0 = Inverse[{{0, I}, {I, 1}}]: 9th; M[0] = {{0, -1}, {-1, -1}}.m0; M[1] = {{1, 0}, {-1, -1}}.m0; M[2] = {{-1, 0}, {-1, -1}}.m0; M[3] = {{0, 1}, {-1, -1}}.m0; M[4] = I*{{0, -1}, {-1, -1}}.m0; M[5] = I*{{1, 0}, {-1, -1}}.m0; M[6] = I*{{-1, 0}, {-1, -1}}.m0; M[7] = I*{{0, 1}, {-1, -1}}.m0; v(n)=M[Mod[n,7]].v(n-1); a(n)=Realpart(v(n)[[1]]).

MATHEMATICA

Clear[M, v, n, a]; m0 = Inverse[{{0, I}, {I, 1}}]; M[0] = {{0, -1}, {-1, -1}}.m0; M[1] = {{1, 0}, {-1, -1}}.m0; M[2] = {{-1, 0}, {-1, -1}}.m0; M[3] = {{0, 1}, {-1, -1}}.m0; M[4] = I*{{0, -1}, {-1, -1}}.m0; M[5] = I*{{1, 0}, {-1, -1}}.m0; M[6] = I*{{-1, 0}, {-1, -1}}.m0; M[7] = I*{{0, 1}, {-1, -1}}.m0; v[0] = {1, 1}; v[n_] := v[n] = M[Mod[n, 7]].v[n - 1]; ar = Table[Re[v[n][[1]]], {n, 0, 50}]

CROSSREFS

Sequence in context: A304263 A305223 A316801 * A305151 A127775 A210953

Adjacent sequences:  A143041 A143042 A143043 * A143045 A143046 A143047

KEYWORD

uned,sign

AUTHOR

Roger L. Bagula, Oct 13 2008

STATUS

approved

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Last modified March 30 06:59 EDT 2020. Contains 333119 sequences. (Running on oeis4.)