Search: id:A160271
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%I A160271
%S A160271 1,2,0,3,0,1,2,0,2,1,4,1,3,2,2,3,0,3,3,4,3,5,1,4,4,6,6,5,4,0,4,4,7,9,10,
%T A160271 8,6,1,5,5,8,11,15,16,13,3,0,5,5,9,12,18,24,26,21,5,2,6,6,10,14,20,29,
%U A160271 39,42,34,7,1,5,6,11,15,23,32,47,63,68,55,4,0,6,7,12,17,25,37,52,76,102
%N A160271 Monotonic justified array of all positive Fibonacci sequences.
%C A160271 Every pair a,b of nonnegative integers occurs in a row. If a>b,
%C A160271 then a is in column 1 and b in column 2. The classical Fibonacci
%C A160271 sequence (A000045) is in row 1; the Lucas sequence (A002878) is in
%C A160271 row 3. Reorderings of the rows and deletions of certain initial terms
%C A160271 give the Wythoff array (A035513), the Stolarsky array (A035506), and
%C A160271 other arrays in which every positive integer occurs exactly once and
%C A160271 every row satisfies the recurrence r(n)=r(n-1)+r(n-2). See the reference
%C A160271 for open questions regarding such arrays.
%D A160271 Clark Kimberling, "Orderings of the set of all positive Fibonacci sequences", 
               in G. E. Bergum et al., editors, Applications of Fibonacci Numbers, 
               Vol. 5 (1993), pp. 405-416.
%H A160271 <a href="classic.html">Classic Sequences</a>
%F A160271 Each row begins with integers a,b satisfying a>b>=0.
%F A160271 The rows are ordered by the following relation on the first
%F A160271 two terms a,b and c,d: (a,b)<(c,d) if and only there exists N
%F A160271 such that aF(n)+bF(n+1)<cF(n)+dF(n+1) for every n>=N, where
%F A160271 F(n)=A000045(n). In terms of r(1)=a and r(2)=b, the remaining
%F A160271 terms of a row are determined by r(n)=r(n-1)+r(n-2).
%e A160271 Northwest corner:
%e A160271 1...0...1...1...2...3...5...8..13..21
%e A160271 2...0...2...2...4...6..10..16..26..42
%e A160271 3...0...3...3...6...9..15..24..39..63
%e A160271 2...1...3...4...7..11..18..29..47..76
%Y A160271 Cf. A000045, A002878, A035513, A035506.
%Y A160271 Sequence in context: A135685 A164658 A079067 this_sequence A065134 A088673 
               A035614
%Y A160271 Adjacent sequences: A160268 A160269 A160270 this_sequence A160272 A160273 
               A160274
%K A160271 nonn,tabl
%O A160271 1,2
%A A160271 Clark Kimberling (ck6(AT)evansville.edu), May 07 2009

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