A230130 Number of permutations of order n with the length of the longest run equal to 7.

2, 28, 362, 4720, 64020, 913440, 13760472, 219040274, 3681354658, 65231186514, 1216489698082, 23832126613268, 489566931234322, 10526180908026522, 236475437787567496, 5541690642862917134, 135258139216049657102, 3433304061341792767884, 90508485528963754208076

Offset: 7

Author

Alois P. Heinz, Oct 10 2013

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 7..450

Crossrefs

Column l=7 of A211318.

A diagonal of A010026.

Programs

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<7,
       add(g(u+j-1, o-j, t+1), j=1..o), 0))
    end:
b:= proc(u, o, t) option remember; `if`(t=7, 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=7..30);

Mathematica

length = 7;
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[tJean-François Alcover, Aug 18 2018, after Alois P. Heinz *)