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A103191 Vector Markov sequence associated with a=1 of the polynomial x^3-2*a*x^3+(a^2+1)*x-2*a (first type). 1
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; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

Tiles are known to be associated with some of the matrices in this reference paper.

REFERENCES

Richard Kenyon et al., Geometry of Self-Affine Tiles II, Indiana Univ. Math. J., Vol. 48, No. 1 (1999), 24-42.

LINKS

Table of n, a(n) for n=0..34.

Richard Kenyon, The Construction of Self-Similar Tilings

Richard Kenyon, Papers.

FORMULA

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].

MATHEMATICA

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}]]

CROSSREFS

Cf. A103193.

Sequence in context: A181274 A115341 A101160 * A324717 A295793 A071607

Adjacent sequences:  A103188 A103189 A103190 * A103192 A103193 A103194

KEYWORD

nonn

AUTHOR

Roger L. Bagula, Mar 18 2005

STATUS

approved

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Last modified May 22 00:25 EDT 2019. Contains 323472 sequences. (Running on oeis4.)