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Search: id:A089077
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| A089077 |
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Alternating 4-Bonacci and theta1 Pisot 4 X 4 matrices in a recursion Adamson matrix procedure. |
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1
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| 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; listen)
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OFFSET
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1,10
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COMMENT
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In 2d an odd even version plotted spirals outward.
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FORMULA
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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]]
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MATHEMATICA
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(* 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}]
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CROSSREFS
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Adjacent sequences: A089074 A089075 A089076 this_sequence A089078 A089079 A089080
Sequence in context: A129402 A134177 A104405 this_sequence A130071 A038540 A084348
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KEYWORD
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sign,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Dec 04 2003
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