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

2, 24, 274, 3204, 39420, 514296, 7137818, 105318770, 1649355338, 27356466626, 479446719522, 8858271760146, 172151975433756, 3511580514677006, 75032190827549478, 1676210011258705592, 39082263260517298658, 949481770375318700914, 23998362106238648271276

Offset

6,1

Links

Alois P. Heinz, Table of n, a(n) for n = 6..450

Maple

g:= proc(u, o, t) option remember; `if`(u+o=0, 1,
       add(g(o+j-1, u-j, 2), j=1..u) +`if`(t<6,
       add(g(u+j-1, o-j, t+1), j=1..o), 0))
    end:
b:= proc(u, o, t) option remember; `if`(t=6, g(u, o, t),
       add(b(o+j-1, u-j, 2), j=1..u)+
       add(b(u+j-1, o-j, t+1), j=1..o))
    end:
a:= n-> add(b(j-1, n-j, 1), j=1..n):
seq(a(n), n=6..30);

Mathematica

length = 6;
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]];
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}]];
a[n_] := Sum[b[j - 1, n - j, 1], {j, 1, n}];
Table[a[n], {n, length, 30}] (* Jean-François Alcover, Aug 18 2018, after Alois P. Heinz *)

Crossrefs

Column l=6 of A211318.

A diagonal of A010026.

Sequence in context: A300399 A221082 A002006 * A355951 A065101 A052739

Adjacent sequences: A230126 A230127 A230128 * A230130 A230131 A230132

Keyword

nonn

Author

Alois P. Heinz, Oct 10 2013

Status

approved