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Search: id:A134564
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| A134564 |
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Array read by antidiagonals: row n consists of numbers whose 4th order Zeckendorf representation has exactly n terms. |
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3
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| 1, 2, 6, 3, 8, 25, 4, 9, 32, 94, 5, 11, 34, 120, 344, 7, 12, 35, 127, 439, 1251, 10, 13, 42, 129, 465, 1596, 4543, 14, 15, 44, 130, 472, 1691
(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, A035513, is the 4rd order Zeckendorf basis, b(1), b(2), b(3),.... Every positive integer has a unique 4th order Zeckendorf representation b(i(1)) + b(i(2)) + . . . + b(i(n)), where |i(h) - i(j)| >=4 for distinct h and j.
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EXAMPLE
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Northwest corner:
1 2 3 4 5 7 10 14 19 26 36 50 69 ...
6 8 9 11 12 13 ...
25 32 34 35 42 44 ...
94 120 127 129 130 156 ...
For example, 32=26+5+1 has 3 terms, so 32 is in row 3.
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CROSSREFS
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Cf. A003269, A136190, A134563.
Adjacent sequences: A134561 A134562 A134563 this_sequence A134565 A134566 A134567
Sequence in context: A076041 A021383 A082154 this_sequence A016637 A133917 A078340
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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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