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A177479
Number of permutations of 1..n avoiding adjacent step pattern up, down, down.
13
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
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
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