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A192089
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Number of permutations of [n] that require a 3-letter alphabet in order to be realized by a shift.
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0
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0, 0, 6, 66, 402, 2028, 8790, 35118, 131982, 475344, 1658382, 5651226, 18912498, 62418180, 203768862, 659487678, 2119617474, 6774043254, 21547968726, 68274910026, 215609878962, 678936947940, 2132568719358, 6683705385078, 20906259913566, 65277851607840
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OFFSET
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2,3
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COMMENTS
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These permutations are those realized by the shift on 3 letters (A192088)
but not by the shift on 2 letters (A059413).
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REFERENCES
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S. Elizalde, The number of permutations realized by a shift, SIAM J. Discrete Math. 23 (2009), 765--786.
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LINKS
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FORMULA
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a(n)=3^(n-2)+sum(psi_3(t)*3^(n-t-1),t=1..n-1)-n*sum(psi_2(t)*2^(n-t-1),t=0..n-1), where psi_N(t) is the number of primitive words of length t over an N-letter alphabet, which is expressible in terms of the Möbius function.
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EXAMPLE
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a(4)=6 because the permutations 1423, 3241, 4132, 2314 3421, 2134 are the only ones of length 4 that require 3 letters in order to be realized by a shift
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CROSSREFS
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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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