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 A083404 Illustration of Viswanath's constant A078416. 0
 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; text; internal format)
 OFFSET 0,2 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 LINKS B. Rittaud, On the Average Growth of Random Fibonacci Sequences, Journal of Integer Sequences, 10 (2007), Article 07.2.4. 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 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). 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 CROSSREFS Cf. Viswanath's constant A078416, V = 1.13198824... Sequence in context: A051485 A077999 A110524 * A232497 A089351 A005380 Adjacent sequences:  A083401 A083402 A083403 * A083405 A083406 A083407 KEYWORD nonn,easy AUTHOR Frank Ellermann, Jun 07 2003 EXTENSIONS More terms from David Wasserman, Nov 01 2004 STATUS approved

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Last modified July 22 15:23 EDT 2019. Contains 325224 sequences. (Running on oeis4.)