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A089076
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Expansion of -x -x^3*(2+x^5-2*x^4) / ( (x-1)*(1+x)*(x^4-x-1) ).
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0
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-1, 0, -2, 2, -4, 4, -6, 7, -11, 14, -20, 26, -37, 50, -70, 95, -132, 181, -251, 345, -477, 657, -908, 1252, -1729, 2385, -3293, 4544, -6273, 8657, -11950, 16493, -22766, 31422, -43372, 59864, -82630, 114051, -157423, 217286, -299916, 413966, -571389, 788674, -1088590, 1502555, -2073944, 2862617
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Actual theta1 Pisot 4 X 4 matrix in an Adamson matrix procedure from eigenvalue polynomial: x^4-x^3-1.
Eigenvalue determinant: Det[{{L,0,0,0},{0,L,0,0},{0,0,L,0},{0,0,0,L}}-m0]=-1+L^3+L^4
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (-1,1,1,1,0,-1).
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FORMULA
| q=1 m0={{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, 0, 0, -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] q=1.38028.... q=N[k-1/k^3, 20] m0={{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, 0, 0, -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: A007212 A067590 A027188 * A123067 A183002 A057601
Adjacent sequences: A089073 A089074 A089075 * A089077 A089078 A089079
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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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