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A255014
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Abelian complexity function of the 4-bonacci word (A254990).
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0
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4, 4, 6, 4, 7, 6, 7, 4, 7, 7, 8, 6, 8, 7, 7, 4, 7, 7, 8, 7, 8, 8, 7, 7, 8, 8, 7, 8, 7, 7, 4, 7, 7, 8, 7, 8, 8, 8, 7, 8, 8, 8, 8, 7, 7, 7, 7, 8, 8, 8, 8, 7, 8, 8, 8, 7, 8, 7, 7, 4, 7, 8, 9, 7, 8, 9, 9, 7, 8, 10, 10, 8, 8, 8, 8, 7, 9, 10, 9, 8, 9, 9, 8, 8, 9, 10, 7, 8, 7, 8, 7, 8, 9, 9, 8, 8, 8, 8, 8, 7
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OFFSET
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1,1
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COMMENTS
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For all n, a(n) either equals 4 or belongs to {6,7,...,16}; value 5 is never attained.
a(n)=4 if and only if n = T(k)+T(k-4)+T(k-8)+T(k-12)+...+T(4+(k mod 4)) for a certain k>=4, where T(i) are tetranacci numbers A000078.
a(n)=6 only for n = 3,6,12.
Each value from the set {7,8,...,16} is attained infinitely often.
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LINKS
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EXAMPLE
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a(1) = 4 because the one letter factor words of A254990 are 0, 1, 2, 3 with the set of occurrence tuples (Parikh vectors) {(1, 0, 0, 0), (0, 1, 0, 0), (0, 0, 1, 0), (0, 0, 0, 1)} of cardinality 4. See the Turek links.
a(2) = 4 because the set of occurrence tuples for the two letter factors 00, 01, 10, 02, 20, 03, 30 of A254990 is {(2, 0, 0, 0), (1, 1, 0, 0), (1, 0, 1, 0), (1, 0, 0, 1)} of cardinality 4. (End)
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CROSSREFS
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Cf. A216190 (abelian complexity of tribonacci word), A254990 (4-bonacci word).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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