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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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6
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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;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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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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LINKS
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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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MATHEMATICA
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DeleteCases[IntegerDigits[Range[200], 2], {___, 0, 0, ___}]
A112309 = Map[DeleteCases[Reverse[#] Fibonacci[Range[Length[#]] + 1], 0] &, DeleteCases[IntegerDigits[-1 + Range[200], 2], {___, 0, 0, ___}]]
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PROG
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(PARI) See Links section.
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CROSSREFS
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KEYWORD
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nonn,tabf,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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