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Search: id:A089135
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| A089135 |
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Alternating 5 Bonacci and 5th power Pisot in a matrix recursive sequence. |
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+0
1
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| 1, 0, 0, 2, 3, -2, -3, 6, 9, -11, -16, 23, 34, -47, -69, 95, 140, -195, -287, 396, 583, -809, -1191, 1648, 2426, -3361, -4948, 6852, 10087, -13970, -20566, 28483, 41931, -58071, -85489, 118398, 174299, -241392, -355364, 492158, 724528, -1003425, -1477187
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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Define two 5 X 5 matrices, mB=[[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]] and mP=[[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1],[1,1,1,1,1]].
The sequence is the (5,5) element of starting with mP and multiplying alternatively the intermediate matrix products with mB and mP.
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FORMULA
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G.f.: x(1+2x^3+x^4-x^9+x^2)/(1+x^2-2x^4+x^10). - R. J. Mathar, Oct 24 2008
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MAPLE
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with(linalg) :
mB := 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]]) :
mP := matrix(5, 5, [[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1], [1, 1, 1, 1, 1]]) :
mt := mP : printf("%d, ", mt[5, 5]) ; for n from 0 to 60 do
mt := evalm(mt&*mB) ; printf("%d, ", mt[5, 5]) ; mt := evalm(mt&*mP) ; printf("%d, ", mt[5, 5]) ; od:
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CROSSREFS
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Cf. A001591.
Sequence in context: A165930 A064895 A120877 this_sequence A038063 A085204 A055375
Adjacent sequences: A089132 A089133 A089134 this_sequence A089136 A089137 A089138
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KEYWORD
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sign
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Dec 05 2003
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EXTENSIONS
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Corrected bad handling of floating point numerics, N. J. A. Sloane (njas(AT)research.att.com), Oct 24 2008
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