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Array T by antidiagonals: T(n,k) = k-th number whose Zeckendorf representation has exactly n terms.
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%I #12 Nov 20 2015 04:12:13

%S 1,2,4,3,6,12,5,7,17,33,8,9,19,46,88,13,10,20,51,122,232,21,11,25,53,

%T 135,321,609,34,14,27,54,140,355,842,1596,55,15,28,67,142,368,931,

%U 2206,4180,89,16,30,72,143,373,965

%N Array T by antidiagonals: T(n,k) = k-th number whose Zeckendorf representation has exactly n terms.

%C A permutation of the natural numbers.

%C Except for initial terms in some cases, (Row 1) = A000045 (Row 2) = A095096 (Row 3) = A059390 (Row 4) = A111458 (Col 1) = A027941 (Col 2) = A005592.

%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>

%e 19 = 13 + 5 + 1 is the 3rd-largest number (after 12 and 17) that has a 3-term Zeckendorf representation; i.e., the (unique) sum of distinct non-neighboring Fibonacci numbers.

%e Northwest corner:

%e 1 2 3 5 8 13

%e 4 6 7 9 10 11

%e 12 17 19 20 25 27

%e 33 46 51 53 54 67

%Y Cf. A035513.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Nov 01 2007