A324137 Number of permutations of [n] that avoid the shuffle pattern s-k-t, where s = 123 and t = 123.

1, 1, 2, 6, 24, 120, 720, 5020, 39790, 352470, 3445032, 36775404, 425282892, 5292245764, 70471602994, 999394962306, 15032677450752, 238984379214960, 4002966472631160, 70448661940661068, 1299478739106621670, 25067231918730741438, 504674373639695198712, 10584965637367018566180

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) (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, A049774.

Sequence in context: A263929 A324139 A324138 * A177552 A177547 A324136

Adjacent sequences: A324134 A324135 A324136 * A324138 A324139 A324140

Keyword

nonn

Author

N. J. A. Sloane, Feb 16 2019

Extensions

More terms from Petros Hadjicostas, Oct 31 2019

Status

approved