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 A265387 Sequence defined by a(1)=a(2)=1 and a(n) = gray(a(n-1)) + gray(a(n-2)), with gray(m) = A003188(m). 3
 1, 1, 2, 4, 9, 19, 39, 78, 157, 316, 629, 1265, 2520, 5053, 10135, 20159, 40508, 80642, 161701, 324346, 645118, 1296264, 2580557, 5174455, 10379095, 20643816, 41480472, 82577840, 165582588, 332131050, 660602145, 1327375184, 2642491049, 5298643189 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS This recurrence is reminiscent of Fibonacci's, except that in each step the arguments are passed through the binary-reflected Gray code mapping, which introduces a degree of pseudo-randomness. Conjecture: The mean growth rate r(n) = (a(2n)/a(n))^(1/n) appears to converge exactly to 2, with the consecutive-terms ratio s(n) = a(n)/a(n-1) exhibiting relatively small (~1%) but persistent fluctuations around the mean value. This contrasts what one might first expect, that sequence's growth rate were similar to that of the Fibonacci sequence, i.e., the golden ratio, since gray(m) just permutes every block of numbers ranging from 2^k to 2^l-1, for any 0>1); a=vector(1000); a[1]=1; a[2]=1; for(n=3, #a, a[n]=gray(a[n-1])+gray(a[n-2])); a CROSSREFS Cf. A000045, A003188, A265385, A265386. Sequence in context: A129784 A125050 A056186 * A293322 A267157 A054135 Adjacent sequences:  A265384 A265385 A265386 * A265388 A265389 A265390 KEYWORD nonn AUTHOR Stanislav Sykora, Dec 07 2015 STATUS approved

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Last modified November 12 12:43 EST 2018. Contains 317109 sequences. (Running on oeis4.)