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Search: id:A103626
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| A103626 |
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4 X 4 vector matrix Markov based on a modification of Veerman's example 7.6 second case. |
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+0
1
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| 1, 1, 1, 1, 1, 2, 2, 2, 1, 3, 4, 4, 1, 5, 6, 7, 1, 8, 10, 11, 1, 12, 16, 18, 1, 19, 24, 28, 1, 29, 38, 43, 1, 44, 58, 67, 1, 68, 88, 102, 1, 103, 136, 156, 1, 157, 206, 239, 1, 240, 314, 363, 1, 364, 480, 554, 1, 555, 728, 844, 1, 845, 1110, 1283, 1, 1284, 1690, 1955, 1, 1956
(list; graph; listen)
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OFFSET
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0,6
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COMMENT
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Characteristic polynomial is: x^4-x^3-x^2-x-2
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REFERENCES
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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
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M = {{1, 0, 0, 0}, {1, 0, 0, 1}, {0, 2, 0, 0}, {0, 1, 1, 0}} v[n_] := v[n] = M.v[n - 1] {a(n), a(n+1), a(n+2), a(n+3)) = Flatten[v[n]]
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MATHEMATICA
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v[0] = {1, 1, 1, 1} M = {{1, 0, 0, 0}, {1, 0, 0, 1}, {0, 2, 0, 0}, {0, 1, 1, 0}} Det[M - x*IdentityMatrix[4] NSolve[Det[M - x*IdentityMatrix[4]] == 0, x] v[n_] := v[n] = M.v[n - 1] a = Flatten[Table[v[n], {n, 0, Floor[200/3]}]]
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CROSSREFS
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Sequence in context: A017125 A063276 A055253 this_sequence A026268 A089258 A004065
Adjacent sequences: A103623 A103624 A103625 this_sequence A103627 A103628 A103629
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KEYWORD
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nonn,uned
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AUTHOR
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Roger Bagula (rlbagulatftn(AT)yahoo.com), Mar 25 2005
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