A299995 - OEIS

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A299995

Number of distinct factorizations of the length-n prefix of the Fibonacci word A003849 into finite Fibonacci words.

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 A359948

Adjacent sequences: A299992 A299993 A299994 * A299996 A299997 A299998

KEYWORD

nonn

AUTHOR

Jeffrey Shallit, Feb 22 2018

STATUS

approved