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A089134
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The matrix sequence made by the lowest fifth power Pisot that is similar to the 5 Bonacci ( Pentafibonacci ).
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0
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-1, 0, 2, -3, 0, 6, -9, 1, 17, -27, 5, 48, -81, 21, 135, -242, 80, 378, -721, 288, 1053, -2142, 999, 2917, -6346, 3375, 8030, -18750, 11178, 21948, -55251, 36451, 59498, -162378, 117383, 159744, -475956, 374097, 423981, -1391417, 1181789, 1109565
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| The sequence is the (5,5) element of the n-th power of the 5 X 5 matrix [[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1],[-1,0,1,-1,-1]].
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FORMULA
| G.f.: -x(1+x)(1-x^2+x^3)/(1+x+x^2-x^3+x^5). - R. J. Mathar, Oct 24 2008
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MAPLE
| with(linalg) : m := matrix(5, 5, [[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1], [-1, 0, 1, -1, -1]]) : for n from 1 to 60 do mt := evalm(m^n) ; printf("%d, ", mt[5, 5]) ; od:
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CROSSREFS
| Cf. A001591.
Sequence in context: A058301 A199601 A097287 * A084257 A185963 A059034
Adjacent sequences: A089131 A089132 A089133 * A089135 A089136 A089137
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KEYWORD
| sign
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Dec 05 2003
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EXTENSIONS
| Corrected flaws of floating point numerics in Mathematica program, N. J. A. Sloane (njas(AT)research.att.com), Oct 24 2008
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