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A324135
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Number of permutations of [n] that avoid the shuffle pattern s-k-t, where s = 12 and t = 123.
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0
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1, 1, 2, 6, 24, 120, 710, 4815, 36650, 308778, 2850294, 28602468, 310041806, 3610879857, 44975227466, 596677473990, 8401332033264, 125140942951896, 1966223504686334, 32501786913873447, 563877339150924866, 10245134152041643818, 194553155073687332550, 3854328529787275833204
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..23.
Sergey Kitaev, Partially Ordered Generalized Patterns, Discrete Math. 298 (2005), no. 1-3, 212-229.
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FORMULA
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Let b(n) = A049774(n) = number of permutations avoiding a consecutive 123 pattern. Then a(n) = Sum_{i = 0..n-1} binomial(n-1,i) (a(n-1-i) + b(i) * a(n-1-i) - b(n-1-i)) for n >= 1 with a(0) = b(0) = 1. [See the recurrence for C_n on p. 220 of Kitaev (2005).] - Petros Hadjicostas, Oct 30 2019
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CROSSREFS
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Cf. A000142, A049774.
Sequence in context: A223034 A177530 A324134 * A177531 A121987 A324132
Adjacent sequences: A324132 A324133 A324134 * A324136 A324137 A324138
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Feb 16 2019
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EXTENSIONS
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More terms from Petros Hadjicostas, Oct 30 2019
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STATUS
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approved
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