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%I #10 Nov 20 2015 04:12:20
%S 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,
%T 267,783,1872,19,14,35,87,273,843
%N Array read by antidiagonals: row n consists of numbers whose 3rd-order Zeckendorf representation has exactly n terms.
%C A permutation of the natural numbers.
%H C. Kimberling, <a href="http://www.fq.math.ca/Scanned/33-1/kimberling.pdf">The Zeckendorf array equals the Wythoff array</a>, Fibonacci Quarterly 33 (1995) 3-8.
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F 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.
%e Northwest corner of the array:
%e 1 2 3 4 6 9 13 19 28 41 60 88 129 ...
%e 5 7 8 10 11 12 ...
%e 18 24 26 27 33 35 ...
%e 59 78 84 86 87 106 ...
%e For example, 26=19+6+1 has 3 terms, so 26 is in row 3.
%Y Cf. A000930, A136189, A134564.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Nov 01 2007, Dec 18 2007
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