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A230129 Number of permutations of order n with the length of longest run equal 6.

%I A230129 #14 Aug 18 2018 08:38:49
%S A230129 2,24,274,3204,39420,514296,7137818,105318770,1649355338,27356466626,
%T A230129 479446719522,8858271760146,172151975433756,3511580514677006,
%U A230129 75032190827549478,1676210011258705592,39082263260517298658,949481770375318700914,23998362106238648271276
%N A230129 Number of permutations of order n with the length of longest run equal 6.
%H A230129 Alois P. Heinz, <a href="/A230129/b230129.txt">Table of n, a(n) for n = 6..450</a>
%p A230129 g:= proc(u, o, t) option remember; `if`(u+o=0, 1,
%p A230129        add(g(o+j-1, u-j, 2), j=1..u) +`if`(t<6,
%p A230129        add(g(u+j-1, o-j, t+1), j=1..o), 0))
%p A230129     end:
%p A230129 b:= proc(u, o, t) option remember; `if`(t=6, g(u, o, t),
%p A230129        add(b(o+j-1, u-j, 2), j=1..u)+
%p A230129        add(b(u+j-1, o-j, t+1), j=1..o))
%p A230129     end:
%p A230129 a:= n-> add(b(j-1, n-j, 1), j=1..n):
%p A230129 seq(a(n), n=6..30);
%t A230129 length = 6;
%t A230129 g[u_, o_, t_] := g[u, o, t] = If[u+o == 0, 1, Sum[g[o + j - 1, u - j, 2], {j, 1, u}] + If[t<length, Sum[g[u + j - 1, o - j, t+1], {j, 1, o}], 0]];
%t A230129 b[u_, o_, t_] := b[u, o, t] = If[t == length, g[u, o, t], Sum[b[o + j - 1, u - j, 2], {j, 1, u}] + Sum[b[u + j - 1, o - j, t + 1], {j, 1, o}]];
%t A230129 a[n_] := Sum[b[j - 1, n - j, 1], {j, 1, n}];
%t A230129 Table[a[n], {n, length, 30}] (* _Jean-François Alcover_, Aug 18 2018, after _Alois P. Heinz_ *)
%Y A230129 Column l=6 of A211318.
%Y A230129 A diagonal of A010026.
%K A230129 nonn
%O A230129 6,1
%A A230129 _Alois P. Heinz_, Oct 10 2013