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A300066
Number of factorizations of the length-n prefix of the Fibonacci word A003849 into a (not strictly) decreasing sequence of finite Fibonacci words.
0
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
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
KEYWORD
nonn
AUTHOR
Jeffrey Shallit, Feb 23 2018
STATUS
approved