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A089077 Alternating 4-Bonacci and theta1 Pisot 4 X 4 matrices in a recursion Adamson matrix procedure. 0
0, 0, 1, 0, 0, -1, 0, -1, -1, -2, -2, -1, -2, 0, -2, 2, 0, 1, 2, 1, 4, -1, 3, -4, -1, -5, -5, -4, -8, -1, -8, 4, -4, 7, 4, 7, 11, 3, 14, -5, 10, -11, -1, -15, -16, -11, -26, 0, -25, 15, -10, 25, 15, 24, 40, 9, 49, -16, 33, -41, -7, -50, -57, -34, -90, 6, -83, 56, -27, 89, 62, 82, 145, 26, 171, -63, 108, -146, -37, -172, -209, -109, -316 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,10

COMMENTS

In 2d an odd even version plotted spirals outward.

LINKS

Table of n, a(n) for n=1..83.

FORMULA

q=1 m0={{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, 0, 0, -q}} m1={{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, 1, 1, q}} a(n) = If[Mod[n, 2]==0, m[n-1].m0, m[n-1].m1][[4, 4]]

MATHEMATICA

(* Adamson's matrix functions alternating x^4-x^3-x^2-x-1 Pisot*) (* and x^4-x^3-1 minimal Pisot theta1*) digits=200 Solve[x^4-x^3-1==0, x] k=theta1 real root q=N[k-1/k^3, 20] m0={{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, 0, 0, -q}} NSolve[x^4-x^3-x^2-x-1==0, x] k1=1.9275619754829254 q1=k1^2-k1-1/k1-1/k1^2 m1={{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, 1, 1, q}} m[n_Integer?Positive] := If[Mod[n, 2]==0, m[n-1].m0, m[n-1].m1] m[0] ={{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}} a=Table[Floor[m[n][[4, 4]]], {n, 1, digits}]

CROSSREFS

Sequence in context: A128580 A104405 A156381 * A203398 A225064 A130071

Adjacent sequences:  A089074 A089075 A089076 * A089078 A089079 A089080

KEYWORD

sign,uned

AUTHOR

Roger L. Bagula, Dec 04 2003

STATUS

approved

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Last modified January 26 05:10 EST 2020. Contains 331273 sequences. (Running on oeis4.)