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Permutation of nonnegative integers formed by ranking fibbinary numbers (A003714) as if they were representatives of the circular binary sequences with forbidden -11- subsequence.
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%I #8 May 01 2014 02:47:40

%S 0,1,2,3,4,5,7,6,8,11,9,10,12,13,18,14,15,19,16,20,17,21,29,22,23,30,

%T 24,31,25,26,32,27,28,33,34,47,35,36,48,37,49,38,39,50,40,41,51,42,52,

%U 43,44,53,45,54,46,55,76,56,57,77,58,78,59,60,79,61,62,80,63,81,64,65

%N Permutation of nonnegative integers formed by ranking fibbinary numbers (A003714) as if they were representatives of the circular binary sequences with forbidden -11- subsequence.

%C Function CircBinSeqNo11Rank gives the position of any 11-free binary sequence in this sequence, where each block consists of Lucas(n-2) sequences of length n: (either the leftmost or the rightmost digit is 1, but not both).

%C In this permutation the Fibonacci numbers themselves (A000045) are fixed.

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%F [seq(CycBinSeqNo11Rank(fibbinary(j)), j=0..233)];

%F a[0] = 0, a[n] = CircBinSeqNo11Rank(fibbinary(n)) for n >= 1.

%e 0; 01,10; 100; 0101,1000,1010; 01001,10000,10010,10100; 010001,010101,100000,100010,100100,101000,101010; etc.

%p CircBinSeqNo11Rank := n -> fibonacci(floor_log_2(n)+1-((-1)^n)) + interpret_as_zeckendorf_expansion(floor(n/(3-((-1)^n))));

%Y Inverse permutation: A056018. For fibbinary function see A048679, interpret_as_zeckendorf_expansion given in A048680.

%K nonn

%O 0,3

%A _Antti Karttunen_, Jun 08 2000