A177479 Number of permutations of 1..n avoiding adjacent step pattern up, down, down.

1, 1, 2, 6, 21, 90, 450, 2619, 17334, 129114, 1067661, 9713682, 96393726, 1036348587, 11998603710, 148842430470, 1969461102357, 27688474234602, 412166988789642, 6476330295597051, 107117619952992966, 1860296912926495938, 33845967939906741213, 643778989807702357314

Offset

0,3

Comments

Suppose j<i, k<j and k<m. To avoid ijkm means not to have four consecutive letters such that the first letter is larger than the second one, the second letter is larger than the third one, and the fourth letter is larger than the third one.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..464

S. Kitaev, Introduction to partially ordered patterns, Discrete Applied Mathematics 155 (2007), 929-944.

Formula

E.g.f.: (exp(3*x/2) + 2*cos(sqrt(3)*x/2)) / (3*cos(sqrt(3)*x/2) - sqrt(3)*sin(sqrt(3)*x/2)). - Vaclav Kotesovec, Aug 23 2014

a(n) ~ n! * (1+exp(Pi/sqrt(3))) * 3^(3*n/2+1/2) / (2*Pi)^(n+1). - Vaclav Kotesovec, Aug 23 2014

Maple

b:= proc(u, o, t) option remember; `if`(u+o=0, 1,
       add(b(u+j-1, o-j, 1), j=1..o)+ `if`(t<2,
       add(b(u-j, o+j-1, `if`(t=0, 0, 2)), j=1..u), 0))
    end:
a:= n-> b(n, 0, 0):
seq(a(n), n=0..30);  # Alois P. Heinz, Oct 07 2013

Mathematica

FullSimplify[Rest[CoefficientList[Series[(E^(3*x/2) + 2*Cos[Sqrt[3]*x/2]) / (3*Cos[Sqrt[3]*x/2] - Sqrt[3]*Sin[Sqrt[3]*x/2]), {x, 0, 20}], x] * Range[0, 20]!]] (* Vaclav Kotesovec, Aug 23 2014 *)

Crossrefs

Column k=0 of A242819.

Columns k=4,6 of A242784.

Sequence in context: A263852 A189243 A033540 * A367100 A147719 A231166

Adjacent sequences: A177476 A177477 A177478 * A177480 A177481 A177482

Keyword

nonn

Author

Submitted independently by Signy Olafsdottir (signy06(AT)ru.is), May 09 2010 (9 terms) and R. H. Hardin, May 10 2010 (17 terms)

Extensions

a(18)-a(23) from Alois P. Heinz, Oct 06 2013

Status

approved