

A177477


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


9



1, 1, 2, 6, 19, 70, 331, 1863, 11637, 81110, 635550, 5495339, 51590494, 524043395, 5743546943, 67478821537, 844983073638, 11240221721390, 158365579448315, 2355375055596386, 36870671943986643, 606008531691619131, 10435226671431973345, 187860338952519968538
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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), 929944.


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(uj, o+j1, [1, 3, 1][t]), j=1..u)+
`if`(t=3, 0, add(b(u+j1, oj, 2), j=1..o)))
end:
a:= n> b(n, 0, 1):
seq(a(n), n=0..25); # Alois P. Heinz, Mar 10 2020


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



