The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A160271 Monotonic justified array of all positive Fibonacci sequences. 4
 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, 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, 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Every pair a,b of nonnegative integers occurs in a row. If a>b, then a is in column 1 and b in column 2. The classical Fibonacci sequence (A000045) is in row 1; the Lucas sequence (A002878) is in row 3. Reorderings of the rows and deletions of certain initial terms give the Wythoff array (A035513), the Stolarsky array (A035506), and other arrays in which every positive integer occurs exactly once and every row satisfies the recurrence r(n)=r(n-1)+r(n-2). See the reference for open questions regarding such arrays. LINKS 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. FORMULA Each row begins with integers a,b satisfying a>b>=0. The rows are ordered by the following relation on the first two terms a,b and c,d: (a,b)<(c,d) if and only there exists N such that aF(n)+bF(n+1)=N, where F(n)=A000045(n). In terms of r(1)=a and r(2)=b, the remaining terms of a row are determined by r(n)=r(n-1)+r(n-2). EXAMPLE Northwest corner: 1...0...1...1...2...3...5...8..13..21 2...0...2...2...4...6..10..16..26..42 3...0...3...3...6...9..15..24..39..63 2...1...3...4...7..11..18..29..47..76 CROSSREFS Cf. A000045, A002878, A035513, A035506. Sequence in context: A135685 A164658 A079067 * A274912 A065134 A088673 Adjacent sequences:  A160268 A160269 A160270 * A160272 A160273 A160274 KEYWORD nonn,tabl AUTHOR Clark Kimberling, May 07 2009 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 18 14:07 EST 2021. Contains 340254 sequences. (Running on oeis4.)