A230131 Number of permutations of order n with the length of longest run equal 8.

2, 32, 462, 6644, 98472, 1523808, 24744720, 422335056, 7575963254, 142706934722, 2819192544786, 58323311592602, 1261634626792744, 28492765388656632, 670804322638496378, 16439609940896532018, 418816100433422180196, 11077009292500273732470

Offset

8,1

Links

Alois P. Heinz, Table of n, a(n) for n = 8..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<8,
       add(g(u+j-1, o-j, t+1), j=1..o), 0))
    end:
b:= proc(u, o, t) option remember; `if`(t=8, 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=8..30);

Mathematica

length = 8;
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=8 of A211318.

A diagonal of A010026.

Sequence in context: A230683 A294328 A109772 * A115418 A163952 A246213

Adjacent sequences: A230128 A230129 A230130 * A230132 A230133 A230134

Keyword

nonn

Author

Alois P. Heinz, Oct 10 2013

Status

approved