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Search: id:A134563
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| A134563 |
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Array read by antidiagonals: row n consists of numbers whose 3rd order Zeckendorf representation has exactly n terms. |
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3
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| 1, 2, 5, 3, 7, 18, 4, 8, 24, 59, 6, 10, 26, 78, 188, 9, 11, 27, 84, 248, 594, 13, 12, 33, 86, 267, 783, 1872, 19, 14, 35, 87, 273, 843
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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A permutation of the natural numbers.
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REFERENCES
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C. Kimberling, "The Zeckendorf array equals the Wythoff array," Fibonacci Quarterly 33(1995) 3-8.
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FORMULA
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Row 1, A000930, is the 3rd order Zeckendorf basis, b(1), b(2), b(3),.... Every positive integer has a unique 3rd order Zeckendorf representation b(i(1)) + b(i(2)) + . . . + b(i(n)), where |i(h) - i(j)| >=3 for distinct h and j.
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EXAMPLE
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Northwest corner of the array:
1 2 3 4 6 9 13 19 28 41 60 88 129 ...
5 7 8 10 11 12 ...
18 24 26 27 33 35 ...
59 78 84 86 87 106 ...
For example, 26=19+6+1 has 3 terms, so 26 is in row 3.
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CROSSREFS
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Cf. A000930, A136189, A134564.
Sequence in context: A082152 A084334 A096878 this_sequence A021398 A115318 A063955
Adjacent sequences: A134560 A134561 A134562 this_sequence A134564 A134565 A134566
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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), Nov 01 2007, Dec 18 2007
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