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A103648
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A Fibonacci isomer vector Markov: matrix characteristic polynomial the same as and Veerman modified sequence but with different results.
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0
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0, 1, 1, 2, 1, 1, 2, 4, 1, 2, 4, 5, 2, 4, 5, 9, 4, 5, 9, 14, 5, 9, 14, 20, 9, 14, 20, 33, 14, 20, 33, 49, 20, 33, 49, 74, 33, 49, 74, 116, 49, 74, 116, 173, 74, 116, 173, 265, 116, 173, 265, 406, 173, 265, 406, 612, 265, 406, 612, 937, 406, 612, 937, 1425, 612, 937, 1425, 2162
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Isomer matrix is: M0 = {{1, 0, 0, 0}, {1, 0, 0, 1}, {0, 2, 0, 0}, {0, 1, 1, 0}} NSolve[Det[M0 - x*IdentityMatrix[4]] == 0, x] Characteristic polynomial for both is x^4-x^3-x^2-x-2=0.
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REFERENCES
| Hausdorff Dimension of Boundaries of Self - Affine Tiles in R^n J. J. P. Veerman, Bol. Soc. Mex. Mat. 3, Vol. 4, No 2, 1998, 159 - 182
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FORMULA
| M = {{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {a0, b, c, d}} {a0, b, c, d} = {-2, 1, 1, 1} v[n_] := v[n] = M.v[n - 1] {a(n), a(n+1), a(n+2), a(n+3)} = v[m]
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MATHEMATICA
| M = {{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {a0, b, c, d}} {a0, b, c, d} = {-2, 1, 1, 1} Det[M - x*IdentityMatrix[4]] NSolve[Det[M - x*IdentityMatrix[4]] == 0, x] v[0] = {0, 1, 1, 2} v[n_] := v[n] = M.v[n - 1] a = Flatten[Table[v[n], {n, 0, Floor[200/3]}]]
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CROSSREFS
| Sequence in context: A056648 A056061 A029265 * A127309 A097853 A160266
Adjacent sequences: A103645 A103646 A103647 * A103649 A103650 A103651
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KEYWORD
| nonn,uned
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AUTHOR
| Roger Bagula (rlbagulatftn(AT)yahoo.com), Mar 25 2005
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