A230131 - OEIS

%I #12 Aug 18 2018 08:38:35

%S 2,32,462,6644,98472,1523808,24744720,422335056,7575963254,

%T 142706934722,2819192544786,58323311592602,1261634626792744,

%U 28492765388656632,670804322638496378,16439609940896532018,418816100433422180196,11077009292500273732470

%N Number of permutations of order n with the length of longest run equal 8.

%H Alois P. Heinz, <a href="/A230131/b230131.txt">Table of n, a(n) for n = 8..450</a>

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

%p        add(g(o+j-1, u-j, 2), j=1..u) +`if`(t<8,

%p        add(g(u+j-1, o-j, t+1), j=1..o), 0))

%p     end:

%p b:= proc(u, o, t) option remember; `if`(t=8, g(u, o, t),

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

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

%p     end:

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

%p seq(a(n), n=8..30);

%t length = 8;

%t 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 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 a[n_] := Sum[b[j - 1, n - j, 1], {j, 1, n}];

%t Table[a[n], {n, length, 30}] (* _Jean-François Alcover_, Aug 18 2018, after _Alois P. Heinz_ *)

%Y Column l=8 of A211318.

%Y A diagonal of A010026.

%K nonn

%O 8,1

%A _Alois P. Heinz_, Oct 10 2013