

A265387


Sequence defined by a(1)=a(2)=1 and a(n) = gray(a(n1)) + gray(a(n2)), 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
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OFFSET

1,3


COMMENTS

This recurrence is reminiscent of Fibonacci's, except that in each step the arguments are passed through the binaryreflected Gray code mapping, which introduces a degree of pseudorandomness.
Conjecture: The mean growth rate r(n) = (a(2n)/a(n))^(1/n) appears to converge exactly to 2, with the consecutiveterms ratio s(n) = a(n)/a(n1) 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^l1, for any 0<k<l.


LINKS

Stanislav Sykora, Table of n, a(n) for n = 1..1000
Wikipedia, Fibonacci number
Wikipedia, Gray code


EXAMPLE

r(10) = 2.000470476732..., r(1000) = 2.000000000203...
s(100) = 2.0058315..., s(101) = 1.9889791..., s(102) = 2.0093437...
s(10000) = 2.0058331..., s(10001) = 1.9889803..., s(10002) = 2.0093413...


PROG

(PARI) gray(m)=bitxor(m, m>>1);
a=vector(1000); a[1]=1; a[2]=1; for(n=3, #a, a[n]=gray(a[n1])+gray(a[n2])); 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



