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A089075
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A theta1 minimal Pisot type valued matrix 4 X 4 4-Bonacci matrix from a root of polynomial of: x^4-x^3-1=0.
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0
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-1, 1, -1, 2, -2, 4, -4, 7, -7, 12, -12, 22, -21, 39, -39, 68, -70, 119, -127, 210, -229, 369, -413, 649, -742, 1143, -1334, 2017, -2393, 3561, -4289, 6293, -7680, 11129, -13739, 19696, -24559, 34879, -43871, 61801, -78324, 109555, -139764, 194291, -249295, 344694, -444496, 611723, -792285
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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FORMULA
| q=-0.724491959000516 m0={{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, 1, 1, q}} a(n) = [Floor[Re[MatrixPower[m0, n][[4, 4]]]]
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MATHEMATICA
| digits=100 NSolve[x^4-x^3-1==0, x] k=1.38027756909761411 q=k^2-k-1/k-1/k^2 m0={{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, 1, 1, q}} m[n_]=MatrixPower[m0, n] a=Table[Floor[Re[m[n][[4, 4]]]], {n, 1, digits}]
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CROSSREFS
| Sequence in context: A062896 A025065 A131524 * A011142 A060029 A100471
Adjacent sequences: A089072 A089073 A089074 * A089076 A089077 A089078
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KEYWORD
| sign,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Dec 04 2003
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