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A177537 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, down, up, up.

%I A177537 #14 Apr 19 2022 11:39:30
%S A177537 1,1,2,6,24,120,720,4985,39440,351000,3470400,37738800,447766925,
%T A177537 5755249449,79663786022,1181466923370,18690124534560,314145239141775,
%U A177537 5590784473674106,105025821614503735,2076805450110696320,43120601826854807940,937944680532722764045
%N A177537 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, down, up, up.
%H A177537 Alois P. Heinz, <a href="/A177537/b177537.txt">Table of n, a(n) for n = 0..175</a>
%F A177537 a(n) ~ c * d^n * n!, where d = 0.9887118103491926984294539697508784179435508781692068887..., c = 1.071215254418408841713627749833237640463228021776737... . - _Vaclav Kotesovec_, Jan 17 2015
%p A177537 b:= proc(u, o, t) option remember; `if`(t>6, 0, `if`(u+o+t<7, (u+o)!,
%p A177537       add(b(u-j, o+j-1, [1, 3, 4, 5, 1, 3][t]), j=1..u)+
%p A177537       add(b(u+j-1, o-j, [2, 2, 2, 2, 6, 7][t]), j=1..o)))
%p A177537     end:
%p A177537 a:= n-> b(n, 0, 1):
%p A177537 seq(a(n), n=0..25);  # _Alois P. Heinz_, Oct 24 2013
%t A177537 b[u_, o_, t_] := b[u, o, t] = If[t > 6, 0, If[u + o + t < 7, (u + o)!,
%t A177537      Sum[b[u - j, o + j - 1, {1, 3, 4, 5, 1, 3}[[t]]], {j, 1, u}] +
%t A177537      Sum[b[u + j - 1, o - j, {2, 2, 2, 2, 6, 7}[[t]]], {j, 1, o}]]];
%t A177537 a[n_] := b[n, 0, 1];
%t A177537 Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Apr 19 2022, after _Alois P. Heinz_ *)
%Y A177537 Columns k=35,49 of A242784.
%K A177537 nonn
%O A177537 0,3
%A A177537 _R. H. Hardin_, May 10 2010
%E A177537 a(17)-a(22) from _Alois P. Heinz_, Oct 24 2013