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Search: id:A137421
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| A137421 |
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Decimal expansion of growth constant in random Fibonacci sequence. |
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+0
1
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| 1, 2, 0, 5, 5, 6, 9, 4, 3, 0, 4, 0, 0, 5, 9, 0, 3, 1, 1, 7, 0, 2, 0, 2, 8, 6, 1, 7, 7, 8, 3, 8, 2, 3, 4, 2, 6, 3, 7, 7, 1, 0, 8, 9, 1, 9, 5, 9, 7, 6, 9, 9, 4, 4, 0, 4, 7, 0, 5, 5, 2, 2, 0, 3, 5, 5, 1, 8, 3, 4, 7, 9, 0, 3, 5, 9, 1, 6
(list; cons; graph; listen)
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OFFSET
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1,2
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REFERENCES
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Benoit Rittaud, Elise Janvresse, Emmanuel Lesigne and Jean-Christophe Novelli, Quand les maths se font discretes, Le Pommier, 2008 (ISBN 978-2-7465-0370-0). See p. 119.
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LINKS
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Elise Janvresse, Benoit Rittaud and Thierry De La Rue, Growth rate for the expected value of a generalized random Fibonacci sequence
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FORMULA
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Comment from Eric Desbiaux (moongerms(AT)wanadoo.fr), Sep 13 2008, Oct 17 2008: In the book by Benoit Rittaud et al. it is stated that this number is cube_root(43/54+sqrt(59/108))+cube_root(43/54-sqrt(59/108))-1/3.
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EXAMPLE
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alpha - 1 = 1.20556943... where alpha is the only real root of alpha^3 = 2*alpha^2 + 1. This is the growth rate of the expected value of a (1/2,1)-random Fibonacci sequence, defined by the relation g_n = | g_{n-1} +/- g_{n-2} |, where the +/- sign is chosen by tossing a balanced coin for each n. The more general case of an unbalanced coin is given by Janvresse, Rittaud and De La Rue.
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MAPLE
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Digits := 80 ; fsolve( x^3-2*x^2-1, x, 2.2..2.3)-1.0 ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 23 2008
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CROSSREFS
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Adjacent sequences: A137418 A137419 A137420 this_sequence A137422 A137423 A137424
Sequence in context: A095245 A086280 A083714 this_sequence A051111 A068558 A082832
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KEYWORD
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easy,nonn,cons
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Apr 16 2008
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 23 2008
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