A300066 Number of factorizations of the length-n prefix of the Fibonacci word A003849 into a (not strictly) decreasing sequence of finite Fibonacci words.

1, 1, 2, 2, 2, 3, 2, 4, 4, 3, 5, 5, 4, 6, 4, 7, 7, 5, 8, 5, 9, 9, 6, 10, 10, 7, 11, 7, 12, 12, 8, 13, 13, 9, 14, 9, 15, 15, 10, 16, 10, 17, 17, 11, 18, 18, 12, 19, 12, 20, 20, 13, 21, 13, 22, 22, 14, 23, 23, 15, 24, 15, 25, 25, 16, 26, 26, 17, 27, 17, 28, 28, 18, 29, 18, 30, 30, 19, 31, 31, 20, 32, 20, 33, 33, 21, 34, 34, 22, 35, 22, 36, 36, 23, 37, 23

Offset

1,3

Comments

The finite Fibonacci words are the prefixes of length F(n) of A003849.

Links

Table of n, a(n) for n=1..96.

Pierre Bonardo, Anna E. Frid, Number of valid decompositions of Fibonacci prefixes, arXiv:1806.09534 [math.CO], 2018.

Example

For n = 7 the two factorizations of 0100101 are (01001)(01) and (010)(01)(01).

Crossrefs

Cf. A299995, which counts arbitrary factorizations, and A000119, which counts strictly decreasing factorizations.

Sequence in context: A029199 A121611 A360106 * A286545 A046798 A329434

Adjacent sequences: A300063 A300064 A300065 * A300067 A300068 A300069

Keyword

nonn

Author

Jeffrey Shallit, Feb 23 2018

Status

approved