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Search: id:A112309
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| A112309 |
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Triangle read by rows: row n gives terms in lazy Fibonacci representation of n. |
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+0
2
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| 1, 2, 1, 2, 1, 3, 2, 3, 1, 2, 3, 2, 5, 1, 2, 5, 1, 3, 5, 2, 3, 5, 1, 2, 3, 5, 1, 3, 8, 2, 3, 8, 1, 2, 3, 8, 2, 5, 8, 1, 2, 5, 8, 1, 3, 5, 8, 2, 3, 5, 8, 1, 2, 3, 5, 8, 2, 5, 13, 1, 2, 5, 13, 1, 3, 5, 13, 2, 3, 5, 13, 1, 2, 3, 5, 13, 1, 3, 8, 13, 2, 3, 8, 13, 1, 2, 3, 8, 13, 2, 5, 8, 13, 1, 2, 5, 8, 13, 1, 3
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Write n as a sum c_2 F_2 + c_3 F_3 + ..., where the F_i are Fibonacci numbers and the c_i are 0 or 1. The lazy expansion is the minimal one in the lexicographic order, in contrast to the Zeckendorf expansion (A035517, A007895), which is the maximal one.
In other words we give preference to the smallest Fibonacci numbers.
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REFERENCES
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W. Steiner, The joint distribution of greedy and lazy Fibonacci expansions, Fib. Q., 43 (No. 1, 2005), 60-69.
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EXAMPLE
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Triangle begins:
1 meaning 1 = 1
2 meaning 2 = 2
1 2 meaning 3 = 1+2
1 3 meaning 4 = 1+3
2 3 meaning 5 = 2+3
1 2 3 meaning 6 = 1+2+3 (and not the Zeckendorf expansion 1+5)
2 5 meaning 7 = 2+5
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CROSSREFS
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Cf. A000045, A112310, A035517, A007895.
Adjacent sequences: A112306 A112307 A112308 this_sequence A112310 A112311 A112312
Sequence in context: A076649 A086289 A077807 this_sequence A060682 A093873 A143773
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KEYWORD
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nonn,tabf,easy
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AUTHOR
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njas, Dec 01 2005
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EXTENSIONS
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Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Dec 01 2005
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