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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

Table of n, a(n) for n=0..28.

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 November 22 10:59 EST 2019. Contains 329389 sequences. (Running on oeis4.)