

A299995


Number of distinct factorizations of the lengthn prefix of the Fibonacci word A003849 into finite Fibonacci words.


1



1, 1, 2, 2, 3, 5, 3, 7, 7, 10, 17, 17, 25, 42, 25, 57, 57, 82, 139, 82, 190, 190, 272, 462, 462, 677, 1139, 677, 1544, 1544, 2221, 3765, 3765, 5500, 9265, 5500, 12544, 12544, 18044, 30588, 18044, 41778, 41778, 59822, 101600, 101600, 148878
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OFFSET

1,3


COMMENTS

The finite Fibonacci words are the prefixes of A003849 of length a Fibonacci number: 0, 01, 010, 01001, etc.


LINKS

Table of n, a(n) for n=1..47.


EXAMPLE

For n = 7, the three factorizations of 0100101 are (01)(0)(01)(01), (01001)(01), and (010)(01)(01).


CROSSREFS

Cf. A003849.
Sequence in context: A317697 A132403 A209167 * A113167 A036014 A289507
Adjacent sequences: A299992 A299993 A299994 * A299996 A299997 A299998


KEYWORD

nonn


AUTHOR

Jeffrey Shallit, Feb 22 2018


STATUS

approved



