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Search: id:A118311
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| A118311 |
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Number of dissimilar square-free quaternary words of length n. |
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+0
1
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| 1, 1, 2, 4, 11, 29, 77, 202, 532, 1395, 3664, 9605, 25192, 66047, 173183, 453998, 1190259, 3120294, 8180124, 21444290, 56217025, 147373441, 386342414, 1012799936, 2655067412
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Sherman Stein and A006156 count ordered square-free(twin-free) ternary words. A060688 counts the dissimilar cases essentially by dividing by 3! (the number of ways to permute a,b,c). A051041 counts ordered square-free quaternary words. A118311 counts the dissimilar cases (beginning with the 4th term) by dividing A051041 by 4!
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REFERENCES
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Sherman Stein, How The Other Half Thinks, 2001, page 149
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EXAMPLE
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a(1) = 1 because a,b,c and d are similar.
a(2) = 1 because aa is not square-free; so ab is the only valid case.
a(3) = 2 counting aba and abc
a(4) = 4 counting abac, abca, abcb and abcd
a(5) = 11 counting abaca,abacb,abcab,abcac,abcba,abacd,abcad,abcbd,abcda,abcdb and abcdc
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CROSSREFS
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Cf. A006156, A060688, A051041.
Sequence in context: A005503 A061860 A093960 this_sequence A132836 A052869 A052831
Adjacent sequences: A118308 A118309 A118310 this_sequence A118312 A118313 A118314
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KEYWORD
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nonn
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AUTHOR
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Alford Arnold (Alford1940(AT)aol.com), Apr 22 2006
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EXTENSIONS
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a(16)-a(25) from Max Alekseyev (maxal(AT)cs.ucsd.edu), Jul 03 2006
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