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A056017
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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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2
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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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.
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LINKS
| Index entries for sequences that are permutations of the natural numbers
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FORMULA
| [seq(CycBinSeqNo11Rank(fibbinary(j)), j=0..233)];
a[0] = 0, a[n] = CircBinSeqNo11Rank(fibbinary(n)) for n >= 1.
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EXAMPLE
| 0; 01,10; 100; 0101,1000,1010; 01001,10000,10010,10100; 010001,010101,100000,100010,100100,101000,101010; etc.
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MAPLE
| CircBinSeqNo11Rank := n -> fibonacci(floor_log_2(n)+1-((-1)^n)) + interpret_as_zeckendorf_expansion(floor(n/(3-((-1)^n))));
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CROSSREFS
| Inverse permutation: A056018. For fibbinary function see A048679, interpret_as_zeckendorf_expansion given in A048680.
Sequence in context: A056018 A191673 A087465 * A091995 A066937 A120750
Adjacent sequences: A056014 A056015 A056016 * A056018 A056019 A056020
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KEYWORD
| nonn
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AUTHOR
| Antti Karttunen Jun 08 2000
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