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Search: id:A165357
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| A165357 |
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Left-justified Wythoff Array. |
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+0
5
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| 1, 0, 2, 1, 1, 2, 1, 3, 0, 3, 2, 4, 2, 0, 4, 3, 7, 2, 3, 0, 3, 5, 11, 4, 3, 4, 1, 4, 8, 18, 6, 6, 4, 4, 1, 3, 13, 29, 10, 9, 8, 5, 5, 2, 4, 21, 47, 16, 15, 12, 9, 6, 5, 2, 5, 34, 76, 26, 24, 20, 14, 11, 7, 6, 2, 4, 55, 123, 42, 39, 32, 23, 17, 12, 8, 7, 3, 5, 89, 199, 68, 63, 52, 37, 28, 19, 14, 9
(list; table; graph; listen)
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OFFSET
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1,3
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COMMENT
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1. Every row satisfies the Fibonacci recurrence: x(n)=x(n-1)+x(n-2).
2. Row n of the Wythoff Array (A035513) is a tail of row n of A165357.
3. Every (a,b) having a>b>=0 occurs exactly once.
4. Every (c,d) having 0<=c<=d occurs exactly once.
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REFERENCES
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C. Kimberling, "Ordering the set of all positive Fibonacci sequences," in Applications of Fibonacci Numbers, vol. 5, Proceedings of the Fifth" International Conference on Fibonacci Numbers and Their Applications, Kluwer, 1993, pages 405-416.
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LINKS
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N. J. A. Sloane, Classic Sequences.
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FORMULA
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Row n is obtained from row n of the Wythoff array (A035513) by applying
reverse Fibonacci recurrence until reaching a pair (a,b) having a>b>=0.
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EXAMPLE
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Northwest corner:
1 0 1 1 2 3
2 1 3 4 7 11
2 0 2 2 4 6
3 0 3 3 6 9
4 0 4 4 8 12
3 1 4 5 9 14
Row 6 of the Wythoff array is (14,23,37,60,...). Reverse recurrence gives
9=23-14, 5=14-9, 4=9-5, 1=5-4, 3=4-1, so that row 6 of A165357 is
(3,1,4,5,9,14,23,37,60,...).
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CROSSREFS
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Cf. A000045, A165359, A165360.
Sequence in context: A133087 A153919 A153905 this_sequence A048996 A111786 A072811
Adjacent sequences: A165354 A165355 A165356 this_sequence A165358 A165359 A165360
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KEYWORD
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nonn,tabl
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu), Sep 16 2009
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