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Search: id:A103191
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| A103191 |
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Vector Markov sequence associated with a=1 of the polynomial x^3-2*a*x^3+(a^2+1)*x-2*a (first type). |
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+0
2
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| 0, 1, 1, 1, 1, 1, 2, 4, 0, 8, 12, 4, 40, 72, 24, 352, 640, 192, 4736, 8704, 2560, 98816, 181760, 53760, 3186688, 5861376, 1732608, 158629888, 291766272, 86245376, 12189433856, 22419865600, 6627262464, 1445910806528, 2659444588544
(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={{1, 0, 1}, {a, a, 0}, {a - 2, 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 = {{1, 0, 1}, {a, a, 0}, {a - 2, 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, 11}]]
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CROSSREFS
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Cf. A103193.
Sequence in context: A011166 A115341 A101160 this_sequence A071607 A095059 A021419
Adjacent sequences: A103188 A103189 A103190 this_sequence A103192 A103193 A103194
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KEYWORD
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nonn
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AUTHOR
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Roger Bagula (rlbagulatftn(AT)yahoo.com), Mar 18 2005
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