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A089062
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A switched recursive matrix method of producing a sequence based on the golden mean and the minimal Pisot real roots.
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1, 0, 1, -1, 1, -1, 0, -2, -1, -1, -2, 0, -2, 0, -1, 1, 0, 0, 1, -1, 1, -1, 0, -2, -1, -1, -2, 0, -2, 0, -1, 1, 0, 0, 1, -1, 1, -1, 0, -2, -1, -1, -2, 0, -2, 0, -1, 1, 0, 0, 1, -1, 1, -1, 0, -2, -1, -1, -2, 0, -2, 0, -1, 1, 0, 0, 1, -1, 1, -1, 0, -2, -1, -1, -2, -1, -2, 0, -1, 1, 0, 0, 1, 0, 1, -1, 0, -2, -1, -1, -2, -1, -2, 0, -1, 1, 0, 1, 1, 1, 1, 0, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,8
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COMMENTS
| A switch based on a method using recursive matrices based on a private communication from Gary Adamson. This method of producing sequences is also mentioned in a Curtis McMullen paper dealing with the irrational rotations associated with Siegel disks. The result is a fractal integer sequence of type ABAB....
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FORMULA
| m[n_Integer?Positive] := If[Mod[n, 2]==0, m[n-1].m0, m[n-1].m1] m[0] = {{1, 0}, {0, 1}} a[n]=Floor[m[n][[2, 2]]]
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MATHEMATICA
| (* Adamson's matrix functions alternating golden mean and minimal Pisot*) digits=200 NSolve[x^3-x-1==0, x] k=-1.32471795724474605 q=k-1/k m0={{0, 1}, {1, q}} NSolve[x^2-x-1==0, x] k1=1.6180339887498949 q1=k1-1/k1 m1={{0, 1}, {1, q1}} m[n_Integer?Positive] := If[Mod[n, 2]==0, m[n-1].m0, m[n-1].m1] m[0] = {{1, 0}, {0, 1}} a=Table[Floor[m[n][[2, 2]]], {n, 1, digits}]
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CROSSREFS
| Sequence in context: A096496 A117209 A035192 * A039980 A194529 A055138
Adjacent sequences: A089059 A089060 A089061 * A089063 A089064 A089065
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KEYWORD
| sign,uned,obsc
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Dec 02 2003
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