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A192088
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Number of permutations of [n] realized by the shift on 3 letters.
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1
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2, 6, 24, 114, 528, 2334, 9528, 36834, 135918, 484206, 1678152, 5694786, 19007808, 62625054, 204215340, 660445914, 2121665016, 6778399914, 21557206332, 68294432778, 215651021484, 679023425238, 2132750062560, 6684084844362, 20907052386534, 65279503654446
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OFFSET
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2,1
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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-1)*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, expressible in terms of the Möbius function.
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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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