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Search: id:A035517
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| A035517 |
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Triangular array read by rows, formed from Zeckendorf expansion of integers: repeatedly subtract the largest Fibonacci number you can until nothing remains. Row n give Z. expansion of n. |
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+0
16
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| 0, 1, 2, 3, 1, 3, 5, 1, 5, 2, 5, 8, 1, 8, 2, 8, 3, 8, 1, 3, 8, 13, 1, 13, 2, 13, 3, 13, 1, 3, 13, 5, 13, 1, 5, 13, 2, 5, 13, 21, 1, 21, 2, 21, 3, 21, 1, 3, 21, 5, 21, 1, 5, 21, 2, 5, 21, 8, 21, 1, 8, 21, 2, 8, 21, 3, 8, 21, 1, 3, 8, 21, 34, 1, 34, 2, 34, 3, 34, 1, 3, 34, 5, 34, 1, 5, 34, 2, 5, 34
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Row n has A007895(n) terms.
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REFERENCES
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D. E. Knuth, Fibonacci multiplication, Appl. Math. Lett. 1 (1988), 57-60.
Zeckendorf, E., Representation des nombres naturels par une somme des nombres de Fibonacci ou de nombres de Lucas, Bull. Soc. Roy. Sci. Liege 41, 179-182, 1972.
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LINKS
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T. D. Noe, Rows n=0..1000 of triangle, flattened
N. J. A. Sloane, Classic Sequences
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EXAMPLE
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0=0; 1=1; 2=2; 3=3; 4=1+3; 5=5; 6=1+5; 7=2+5; 8=8; 9=1+8; 10=2+8; ... so triangle begins
0
1
2
3
1 3
5
1 5
2 5
8
1 8
2 8
3 8
1 3 8
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CROSSREFS
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Cf. A014417, A007895, A035514, A035515, A035516.
Sequence in context: A119348 A050375 A154722 this_sequence A099471 A121775 A127951
Adjacent sequences: A035514 A035515 A035516 this_sequence A035518 A035519 A035520
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KEYWORD
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nonn,easy,tabf,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Dec 13 1999
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