A056017 Permutation of nonnegative integers formed by ranking fibbinary numbers (A003714) as if they were representatives of the circular binary sequences with forbidden -11- subsequence.

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, 24, 31, 25, 26, 32, 27, 28, 33, 34, 47, 35, 36, 48, 37, 49, 38, 39, 50, 40, 41, 51, 42, 52, 43, 44, 53, 45, 54, 46, 55, 76, 56, 57, 77, 58, 78, 59, 60, 79, 61, 62, 80, 63, 81, 64, 65

Offset: 0

Author

Antti Karttunen, Jun 08 2000

Keywords

• nonn

Comments

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).

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

Examples

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

Links

• Index entries for sequences that are permutations of the natural numbers

Crossrefs

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

Programs

Maple

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

Formula

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

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