A324139 Number of permutations of [n] that avoid the shuffle pattern s-k-t, where s = 132 and t = 132.

1, 1, 2, 6, 24, 120, 720, 5020, 39720, 350496, 3404208, 36024468, 412029720, 5060178264, 66366899712, 925327730484, 13661323157928, 212844811207536, 3489053207930640, 60017166553937508, 1080783290762095320, 20331614843059904712, 398783856019074779808, 8140910725545925463172

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) = A111004(n) = number of permutations avoiding a consecutive 132 pattern. Then a(n) = Sum_{i = 0..n-1} binomial(n-1,i) (2*b(i)*a(n-1-i) - b(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, A111004.

Sequence in context: A177551 A177535 A263929 * A324138 A324137 A177552

Adjacent sequences: A324136 A324137 A324138 * A324140 A324141 A324142

Keyword

nonn

Author

N. J. A. Sloane, Feb 16 2019

Extensions

More terms from Petros Hadjicostas, Oct 30 2019

Status

approved