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Search: id:A107381
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| A107381 |
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Quartic Binet sequence for characteristic real root polynomial:x^4-3*x^2+3*x+1. |
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+0
1
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| 4, 3, 9, 17, 40, 92, 215, 506, 1200, 2861, 6848, 16436, 39523, 95162, 229328, 552977, 1333920, 3218612, 7767575, 18747986, 45254200, 109241261, 263712248, 636626156, 1536900483, 3710323442
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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real roots: {{x -> -0.618034}, {x -> -0.414214}, {x -> 1.61803}, {x -> 2.41421}}
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FORMULA
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n=3 a(m) = n*(b4^m + b3^m + b1^m + b2^m)/(b4 + b3 + b2 + b1)
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MATHEMATICA
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n = 3; b4 = x /. NSolve[x^4 - n*x^3 + n*x + 1 == 0, x][[4]] b3 = x /. NSolve[x^4 - n*x^3 + n*x + 1 == 0, x][[3]] b2 = x /. NSolve[x^4 - n*x^3 + n*x + 1 == 0, x][[2]] b1 = x /. NSolve[x^4 - n*x^3 + n*x + 1 == 0, x][[1]] digits = 25 a = Table[n*(b4^m + b3^m + b1^m + b2^m)/(b4 + b3 + b2 + b1), {n, 0, digits}]
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CROSSREFS
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Adjacent sequences: A107378 A107379 A107380 this_sequence A107382 A107383 A107384
Sequence in context: A094728 A131805 A103218 this_sequence A132192 A075563 A081617
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KEYWORD
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nonn,uned
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AUTHOR
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Roger L.Bagula (rlbagulatftn(AT)yahoo.com), May 24 2005
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