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A089062 A switched recursive matrix method of producing a sequence based on the golden mean and the minimal Pisot real roots. 0
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; text; internal format)
OFFSET

1,8

COMMENTS

A switch based on a method using recursive matrices based on a private communication from Gary W. 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....

LINKS

Table of n, a(n) for n=1..103.

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]]]

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}]

CROSSREFS

Sequence in context: A117209 A035192 A229653 * A282634 A039980 A194529

Adjacent sequences:  A089059 A089060 A089061 * A089063 A089064 A089065

KEYWORD

sign,uned,obsc

AUTHOR

Roger L. Bagula, Dec 02 2003

STATUS

approved

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Last modified December 15 01:20 EST 2018. Contains 318141 sequences. (Running on oeis4.)