A324135 Number of permutations of [n] that avoid the shuffle pattern s-k-t, where s = 12 and t = 123.

1, 1, 2, 6, 24, 120, 710, 4815, 36650, 308778, 2850294, 28602468, 310041806, 3610879857, 44975227466, 596677473990, 8401332033264, 125140942951896, 1966223504686334, 32501786913873447, 563877339150924866, 10245134152041643818, 194553155073687332550, 3854328529787275833204

Offset

0,3

Links

Table of n, a(n) for n=0..23.

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