A132917 Order set of the first 300 infinite truncated Fibonacci Words where a(n) is the number of terms (ones and zeros) truncated from the left hand side of the word.

233, 89, 178, 34, 267, 123, 212, 68, 157, 13, 246, 102, 191, 47, 280, 136, 225, 81, 170, 26, 259, 115, 204, 60, 293, 149, 5, 238, 94, 183, 39, 272, 128, 217, 73, 162, 18, 251, 107, 196, 52, 285, 141, 230, 86, 175, 31, 264, 120, 209, 65, 298, 154, 10, 243, 99, 188

Offset: 0

Author

Kenneth J Ramsey, Sep 05 2007

Keywords

• nonn
• uned

Comments

The sequence can also be built up from left to right directly (without having to make insertions) as follows:

a(0) equals greatest odd Fibonacci number less than n, i.e., [a(0) = F(2m)]

The rule for a(n+1) is according to the following (first listed takes priority):

a(n+1) = a(n) + F(2m) if less than or equal to n

a(n+1) = a(n) - F(2m-1) if greater than 0

a(n+1) = a(n) + F(2m-2)

Continue until all n terms have been included in the sequence.

Examples

			4 appears between 2 and 1 in the sequence because the greatest odd Fibonacci number less than 4 is 2 and the greatest even Fibonacci number less than 4 is 3
		

Links

• Kenneth J Ramsey, Sep 05 2007, Table of n, a(n) for n = 0..299

Crossrefs

Cf. A132828.

Formula

The sequence is generated starting with {2,1} and the numbers 3,4,5,..n are inserted in order into the sequence using the following rules: If n is an even Fibonacci number, it is inserted after the last term If n is an odd Fibonacci number, it is inserted before the first term If n is not a Fibonacci number, it is inserted between the adjacent terms, n - GF(even) and n-GF(odd) where GF(odd) and GF(even) are respectively the greatest odd and even Fibonacci numbers less than n.