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A095903 Lexical ordering of the lazy Fibonacci representations. 3
1, 2, 3, 4, 5, 7, 6, 8, 9, 12, 10, 13, 15, 20, 11, 14, 16, 21, 17, 22, 25, 33, 18, 23, 26, 34, 28, 36, 41, 54, 19, 24, 27, 35, 29, 37, 42, 55, 30, 38, 43, 56, 46, 59, 67, 88, 31, 39, 44, 57, 47, 60, 68, 89, 49, 62, 70, 91, 75, 96, 109, 143, 32, 40, 45, 58, 48, 61, 69, 90, 50, 63 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A permutation of the natural numbers. As suggested by the example, the numbers can be generated as a graph consisting of two components, each being a tree. One tree has root 1 and consists of the numbers in the lower Wythoff sequence, A000201; the other has root 2 and consists of the numbers in the upper Wythoff sequence, A001950.  (One could start with 0 and have a single tree instead of two components.)

Regard generations g(n) of the graph as rows of an array (see Example); then |g(n)| = 2^n.  Every row includes exactly two Fibonacci numbers; specifically, row n includes F(2n) and F(2n+1). - Clark Kimberling, Mar 11 2015

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..4000

EXAMPLE

Start with 1,2. Suffix the next two Fibonacci numbers, getting 1+2, 1+3; 2+3, 2+5. Suffix the next two Fibonacci numbers, getting 1+2+3, 1+2+5, 1+3+5, 1+3+8; 2+3+5, 2+3+8, 2+5+8, 2+5+13. Continue, obtaining

row 1:  1,2

row 2:  3,4,5,7

row 3:  6,8,9,12,10,13,15,20

row 4:  11,14,16,21,17,22,25,33,18,23,26,34,28,36,41,54

MATHEMATICA

Map[Total, Fibonacci[Flatten[NestList[Flatten[Map[{Join[#, {Last[#]+1}], Join[#, {Last[#]+2}]}&, #], 1]&, {{2}, {3}}, 7], 1]]]  (* Peter J. C. Moses, Mar 06 2015 *)

CROSSREFS

Cf. A000045, A095791, A000201, A001950, A255773 (the 1-tree), A255774 (the 2-tree).

Sequence in context: A267111 A161919 A269391 * A267112 A269392 A166277

Adjacent sequences:  A095900 A095901 A095902 * A095904 A095905 A095906

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jun 12 2004

STATUS

approved

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Last modified August 18 16:08 EDT 2017. Contains 290727 sequences.