

A345717


Orders of abelian cubes in the tribonacci word A080843.


1



4, 6, 7, 11, 13, 17, 18, 20, 24, 26, 27, 30, 31, 33, 37, 38, 40, 41, 42, 43, 44, 48, 50, 51, 55, 57, 61, 62, 63, 64, 68, 70, 74, 75, 77, 79, 81, 85, 86, 87, 88, 92, 94, 95, 98, 99, 101, 105, 107, 108, 111, 112, 114, 116, 118, 119, 122, 123, 125, 129, 131, 132
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OFFSET

1,1


COMMENTS

An abelian cube is a word of the form x x' x'', where x' and x'' are permutations of x, like the English word "deeded". The order of an abelian cube is the length of x.


LINKS



FORMULA

There is a deterministic finite automaton of 1169 states that takes n in its tribonacci representation as input and accepts if and only if there is an abelian cube of order n. It can be obtained with the Walnut theoremprover.


EXAMPLE

Here are the earliestappearing abelian cubes of the first few orders:
n = 4: 2010.0102.0102
n = 6: 102010.010201.010201
n = 7: 0102010.0102010.1020100
n = 11: 02010010201.01020100102.01020100102


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



