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

Author

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

Keywords

• nonn

Comments

Suppose j

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.

Crossrefs

Column k=0 of A242819.

Columns k=4,6 of A242784.

Programs

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 *)

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

Extensions

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

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