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Search: id:A103193
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| A103193 |
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Vector Markov sequence associated with a=1 of the polynomial x^3-(2*a+1)*x^2+(a^2+2*a+1)*x+(a^2+2*a-1) (second type). |
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+0
2
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| 0, 1, 1, 1, 1, 1, 5, 1, -5, -7, 1, -1, 33, 1, -1, -255, 1, 255, 1, 1, -2049, 16385, 1, -32769, 262145, 1, -524289, 1, 1, -8388609, -268435455, 1, 268435455, 8589934593, 1, -1, -549755813887, 1, -1, 70368744177665, 1, -70368744177665, 1, 1, 9007199254740991, -1152921504606846975
(list; graph; listen)
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OFFSET
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0,7
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COMMENT
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Tiles are known to be associated with some of the matrices in this reference paper.
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REFERENCES
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Richard Kenyon et al., Geometry of Self-Affine Tiles II, Indiana Univ. Math. J., Vol. 48, No. 1 (1999), 24-42.
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LINKS
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Richard Kenyon, The Construction of Self-Similar Tilings
Richard Kenyon, Papers.
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FORMULA
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M = {{2, 0, 1}, {a - 1, a, 0}, {a - 3, 1, a - 1}}; vector function v[n]=M.v[n-1]; a(n) = sequence of vector components of M^n.v[0].
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MATHEMATICA
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a = 1; M1 = {{2, 0, 1}, {a - 1, a, 0}, {a - 3, 1, a - 1}}; v[0] = {0, 1, 1}; v[1] = {1, 1, 1}; v[n_] := v[n] = MatrixPower[M1, n].v[n - 1]; b = Flatten[Table[v[n], {n, 0, 15}]]
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CROSSREFS
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Cf. A103191.
Sequence in context: A054244 A093562 A081774 this_sequence A011093 A062176 A129769
Adjacent sequences: A103190 A103191 A103192 this_sequence A103194 A103195 A103196
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KEYWORD
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sign
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AUTHOR
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Roger Bagula (rlbagulatftn(AT)yahoo.com), Mar 18 2005
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