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Search: id:A107382
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| A107382 |
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Quartic Binet sequence for characteristic real root polynomial:x^4-4*x^2+4*x+1. |
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+0
1
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| 4, 4, 16, 52, 188, 684, 2512, 9244, 34052, 125476, 462416, 1704212, 6280892, 23148428, 85314448, 314430012, 1158845444, 4270975556, 15740867728, 58013659124, 213811888828, 788013108844, 2904256931152, 10703766510172
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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These real quartic roots give aperiodic tilings as well. real roots: {{x -> -0.749118}, {x -> -0.27133}, {x -> 1.3349}, {x -> 3.68554}}
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FORMULA
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n=4 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 = 4; 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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Sequence in context: A038234 A099462 A092266 this_sequence A038788 A010099 A060691
Adjacent sequences: A107379 A107380 A107381 this_sequence A107383 A107384 A107385
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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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