A177477 Number of permutations of 1..n avoiding adjacent step pattern up, down, up.

1, 1, 2, 6, 19, 70, 331, 1863, 11637, 81110, 635550, 5495339, 51590494, 524043395, 5743546943, 67478821537, 844983073638, 11240221721390, 158365579448315, 2355375055596386, 36870671943986643, 606008531691619131, 10435226671431973345, 187860338952519968538

Offset

0,3

Comments

Suppose a < b, c < b, and c < d. To avoid abcd means not to have four consecutive letters such that the first letter is less than the second one, the third letter is less than the second one, and the third letter is less than the last one.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..468

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

Formula

a(n) ~ c * d^n * n!, where d = A245758 = 0.7827041801715217018447074977..., c = 2.035127405829990832658061124449458067... . - Vaclav Kotesovec, Aug 22 2014

Maple

b:= proc(u, o, t) option remember; `if`(u+o=0, 1,
       add(b(u-j, o+j-1, [1, 3, 1][t]), j=1..u)+
      `if`(t=3, 0, add(b(u+j-1, o-j, 2), j=1..o)))
    end:
a:= n-> b(n, 0, 1):
seq(a(n), n=0..25);  # Alois P. Heinz, Mar 10 2020

Mathematica

b[u_, o_, t_] := b[u, o, t] = If[u + o == 0, 1,
     Sum[b[u - j, o + j - 1, {1, 3, 1}[[t]]], {j, 1, u}] +
     If[t == 3, 0, Sum[b[u + j - 1, o - j, 2], {j, 1, o}]]];
a[n_] := b[n, 0, 1];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Mar 08 2022, after Alois P. Heinz *)

Crossrefs

Column k=0 of A227884.

Column k=5 of A242784.

Cf. A227883, A245758.

Sequence in context: A150114 A199128 A150115 * A150116 A150117 A038392

Adjacent sequences: A177474 A177475 A177476 * A177478 A177479 A177480

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

a(0)=1 prepended by Alois P. Heinz, Mar 10 2020

Status

approved