

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
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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 nth 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 nth term.)  Benoit Rittaud (rittaud(AT)math.univparis13.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 x1=1.20556943..., where x is the only real number solution of the equation x^3 = 2x^2 + 1.  Benoit Rittaud (rittaud(AT)math.univparis13.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**(N1); 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



