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A177526 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, up, down. 2

%I #16 Apr 19 2022 11:02:42

%S 1,1,2,6,24,120,680,4480,33600,285434,2684680,27812170,313926560,

%T 3842611240,50625902600,714873188122,10764733339179,172258243070682,

%U 2918333808555034,52191694000877878,982479378895814520,19419959862935129834,402131210857811703926

%N Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, up, down.

%H Alois P. Heinz, <a href="/A177526/b177526.txt">Table of n, a(n) for n = 0..170</a>

%F a(n) ~ c * d^n * n!, where d = 0.94123983763344712685016041467..., c = 1.3558011859159420827133973526... . - _Vaclav Kotesovec_, Jan 17 2015

%p b:= proc(u, o, t) option remember; `if`(t>5, 0, `if`(u+o=0, 1,

%p add(b(u-j, o+j-1, [1, 3, 4, 1, 6][t]), j=1..u)+

%p add(b(u+j-1, o-j, [2, 2, 2, 5, 2][t]), j=1..o)))

%p end:

%p a:= n-> `if`(n=0, 1, add(b(j-1, n-j, 1), j=1..n)):

%p seq(a(n), n=0..25); # _Alois P. Heinz_, Oct 21 2013

%t b[u_, o_, t_] := b[u, o, t] = If[t > 5, 0, If[u + o + t < 6, (u + o)!,

%t Sum[b[u - j, o + j - 1, {1, 3, 4, 1, 6}[[t]]], {j, 1, u}] +

%t Sum[b[u + j - 1, o - j, {2, 2, 2, 5, 2}[[t]]], {j, 1, o}]]];

%t a[n_] := b[n, 0, 1];

%t Table[a[n], {n, 0, 25}] (* _Jean-Fran├žois Alcover_, Apr 19 2022, after _Alois P. Heinz_ *)

%Y Columns k=18,22 of A242784.

%K nonn

%O 0,3

%A _R. H. Hardin_, May 10 2010

%E a(17)-a(22) from _Alois P. Heinz_, Oct 21 2013

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Last modified September 23 17:42 EDT 2023. Contains 365554 sequences. (Running on oeis4.)