A324136 Number of permutations of [n] that avoid the shuffle pattern s-k-t, where s = 12 and t = 1234.

1, 1, 2, 6, 24, 120, 720, 5025, 39926, 355538, 3505864, 37917861, 446320694, 5680229144, 77727692650, 1138088663183, 17755248475106, 294036917039062, 5151744388600780, 95211200654845109, 1851125559811374946, 37769517149637845508, 806945623696758245062

Offset

0,3

Links

Table of n, a(n) for n=0..22.

Sergey Kitaev, Partially Ordered Generalized Patterns, Discrete Math. 298 (2005), no. 1-3, 212-229.

Formula

Let b(n) = A117158(n) = number of permutations avoiding a consecutive 1234 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, A117158.

Sequence in context: A324137 A177552 A177547 * A177548 A193935 A177534

Adjacent sequences: A324133 A324134 A324135 * A324137 A324138 A324139

Keyword

nonn

Author

N. J. A. Sloane, Feb 16 2019

Extensions

More terms from Petros Hadjicostas, Oct 30 2019

Status

approved