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A123186
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3 X 3 switched vector matrix Markov from a Burau representation of B4->GL[3,Z] with condition that: MatrixPower[M1.M2.M3, 4]=n^4*I[3].
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0
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1, 1, 1, -2, -2, -2, 0, 0, 0, -8, -8, -8, 1112, 1112, 1112, -16336, -16336, -16336, 29760, 29760, 29760, 108608, 108608, 108608, 112587520, 112587520, 112587520, -3584451200, -3584451200, -3584451200, 17790850560, 17790850560, 17790850560, 208254684160, 208254684160
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| The switched matrix counts up with n: Table[Det[M[n]], {n, 1, 50}] {-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20, -21, -22, -23, -24, -25, -26, -27, -28, -29, -30, -31, -32, -33, -34, -35, -36, -37, -38, -39, -40, -41, -42, -43, -44, -45, -46, -47, -48, -49, -50}
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REFERENCES
| Brian Mangum and Patrick Shanahan, Three-dimensional representations of punctured torus bundles, Journal of Knot Theory and Its Ramifications, 6 (1997), no. 6, 817-825.
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FORMULA
| M1 = {{-n, 1, 0}, {0, 1, 0}, {0, 0, 1}}; M2 = {{1, 0, 0}, {n, -n, 1}, {0, 0, 1}}; M3 = {{1, 0, 0}, {0, 1, 0}, {0, n, -n}}; M[n_] := If[Mod[n, 3] == 1, M1, If[Mod[n, 3] == 2, M2, M3]] v[1] = {1, 0, 0} v[n_] := v[n] = M[n].v[n - 1] a(n) = v[n][[1]]
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MATHEMATICA
| M1 = {{-n, 1, 0}, {0, 1, 0}, {0, 0, 1}}; M2 = {{1, 0, 0}, {n, -n, 1}, {0, 0, 1}}; M3 = {{1, 0, 0}, {0, 1, 0}, {0, n, -n}}; M[n_] := If[Mod[n, 3] == 1, M1, If[Mod[n, 3] == 2, M2, M3]] v[1] = {1, 0, 0} v[n_] := v[n] = M[n].v[n - 1] a1 = Table[v[n][[1]], {n, 1, 50}]
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CROSSREFS
| Sequence in context: A037865 A039969 A039967 * A127323 A132896 A089789
Adjacent sequences: A123183 A123184 A123185 * A123187 A123188 A123189
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KEYWORD
| uned,sign
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AUTHOR
| Roger Bagula and Gary Adamson (rlbagulatftn(AT)yahoo.com), Oct 03 2006
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