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 A324135 Number of permutations of [n] that avoid the shuffle pattern s-k-t, where s = 12 and t = 123. 0
 1, 1, 2, 6, 24, 120, 710, 4815, 36650, 308778, 2850294, 28602468, 310041806, 3610879857, 44975227466, 596677473990, 8401332033264, 125140942951896, 1966223504686334, 32501786913873447, 563877339150924866, 10245134152041643818, 194553155073687332550, 3854328529787275833204 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Sergey Kitaev, Partially Ordered Generalized Patterns, Discrete Math. 298 (2005), no. 1-3, 212-229. FORMULA 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 CROSSREFS Cf. A000142, A049774. Sequence in context: A223034 A177530 A324134 * A177531 A121987 A324132 Adjacent sequences: A324132 A324133 A324134 * A324136 A324137 A324138 KEYWORD nonn AUTHOR N. J. A. Sloane, Feb 16 2019 EXTENSIONS More terms from Petros Hadjicostas, Oct 30 2019 STATUS approved

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Last modified March 31 17:28 EDT 2023. Contains 361668 sequences. (Running on oeis4.)