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A083404
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Illustration of Viswanath's constant A078416.
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0
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1, 2, 6, 14, 32, 82, 196, 464, 1142, 2746, 6576, 15976, 38484, 92544, 223790, 539402, 1299184, 3136178, 7560760, 18222032, 43956888, 105980632, 255487040, 616137680, 1485562228, 3581617536, 8636505982, 20823634954, 50206996848
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n) is the sum of the absolute values of the (2+n)-th terms in 2^n "random Fibonacci sequences" using either addition or subtraction.
Viswanath's constant V approximates a(15) = 223790 by (2*V)^15 or about 210416.
Approximating a(19) = 7560760 by (2*V)^19 or about 5527978 appears to be bad, why?
Viswanath's constant is not relevant for this sequence, since these two questions are different: what is the growth rate of almost random Fibonacci sequences, what is the average value of the n-th term of such a random Fibonacci sequence? (I've just submitted a paper to Journal of Number Theory to prove that the two problems have different solutions. I'm currently preparing a second paper which gives the explicit value of the constant involved in the context of average value of n-th term.) - Benoit Rittaud (rittaud(AT)math.univ-paris13.fr), Mar 10 2006
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LINKS
| B. Rittaud, On the Average Growth of Random Fibonacci Sequences, Journal of Integer Sequences, 10 (2007), Article 07.2.4.
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FORMULA
| This sequence is exponentially increasing, with growth rate equal to x-1=1.20556943..., where x is the only real number solution of the equation x^3 = 2x^2 + 1. - Benoit Rittaud (rittaud(AT)math.univ-paris13.fr), Jan 20 2007
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EXAMPLE
| a(2) = 6 = 1 +1 +3 +abs(-1), the 2^2 last terms in (1,1,0,1), (1,1,0,1), (1,1,2,3), (1,1,2,-1).
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PROG
| /*REXX*/ A.1 = 1; B.1 = 1; SSS = 1; do N = 1 to 18; M = 2**(N-1); Sum = 0; do K = 1 to M; L = K + M; ADD = A.K + B.K; SUB = A.K - B.K; A.K = B.K; A.L = B.K; B.K = ADD; B.L = SUB; Sum = Sum + abs( ADD ) + abs( SUB ); end K; SSS = SSS Sum; end N; say SSS
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CROSSREFS
| Cf. Viswanath's constant A078416, V = 1.13198824...
Sequence in context: A051485 A077999 A110524 * A089351 A005380 A124612
Adjacent sequences: A083401 A083402 A083403 * A083405 A083406 A083407
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KEYWORD
| nonn,easy
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AUTHOR
| Frank.Ellermann(AT)t-online.de, Jun 07 2003
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EXTENSIONS
| More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Nov 01 2004
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