A177483 Number of permutations avoiding the pattern 1231'.

1, 1, 2, 6, 20, 85, 420, 2443, 16136, 120222, 993770, 9042451, 89725944, 964693717, 11168801294, 138549935190, 1833264311504, 25773751694161, 383664263687964, 6028473673565695, 99710105438401940, 1731651866118338766, 31505416776034601510, 599259743707431667279

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..460

Sergey Kitaev, Segmented partially ordered generalized patterns, Theoretical Computer Science 349(3) (2005), 420-428; see Proposition 7 (p. 424).

Formula

E.g.f.: x*exp(x/2) / (cos(sqrt(3)*x/2) - sin(sqrt(3)*x/2) / sqrt(3)) + 1.

a(n) ~ n! * exp(Pi/(3*sqrt(3))) * (3*sqrt(3)/(2*Pi))^n. - Vaclav Kotesovec, Aug 24 2014

Example

For n = 4, we have a(4) = 20 because the only bad permutations are 1234, 1342, 1243 and 2341.

Mathematica

CoefficientList[Series[x*E^(x/2)/(Cos[Sqrt[3]*x/2] - Sin[Sqrt[3]*x/2] / Sqrt[3]) + 1, {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Aug 24 2014*)

Crossrefs

Sequence in context: A177480 A365229 A089179 * A004104 A304932 A293032

Adjacent sequences: A177480 A177481 A177482 * A177484 A177485 A177486

Keyword

nonn

Author

Signy Olafsdottir (signy06(AT)ru.is), May 09 2010, May 14 2010

Extensions

Offset corrected by Vaclav Kotesovec, Aug 24 2014

More terms from Vaclav Kotesovec, Aug 24 2014

Status

approved