Identifier
- St001423: Binary words ⟶ ℤ
Values
=>
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1=>0
00=>0
01=>0
10=>0
11=>0
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111110010=>1
111110011=>1
111110100=>1
111110101=>1
111110110=>1
111110111=>1
111111000=>3
111111001=>2
111111010=>2
111111011=>2
111111100=>2
111111101=>2
111111110=>2
111111111=>3
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Description
The number of distinct cubes in a binary word.
A factor of a word is a sequence of consecutive letters. This statistic records the number of distinct non-empty words $u$ such that $uuu$ is a factor of the word.
A factor of a word is a sequence of consecutive letters. This statistic records the number of distinct non-empty words $u$ such that $uuu$ is a factor of the word.
References
[1] Number of cubefree words of length n on two letters. OEIS:A028445
Code
def statistic(w): lst = [] for i in range(len(w)): for l in range(1, (len(w)-i)//3+1): if w[i:i+l] == w[i+l:i+2*l] == w[i+2*l:i+3*l]: lst.append(tuple(w[i:i+l])) return len(set(lst))
Created
Jun 20, 2019 at 00:32 by Martin Rubey
Updated
Jun 20, 2019 at 08:38 by Martin Rubey
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