A230133 Number of permutations of order n with the length of longest run equal 10.

2, 40, 698, 11908, 206388, 3690960, 68577600, 1327697280, 26812356480, 564796979240, 12403183337690, 283718956204402, 6753363090218970, 167092903876164794, 4292602805804464576, 114374394103260000000, 3157276569203744863200, 90202107365906127228000

Offset

10,1

Links

Alois P. Heinz, Table of n, a(n) for n = 10..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<10,
       add(g(u+j-1, o-j, t+1), j=1..o), 0))
    end:
b:= proc(u, o, t) option remember; `if`(t=10, 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=10..30);

Mathematica

length = 10;
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=10 of A211318.

A diagonal of A010026.

Sequence in context: A012807 A127186 A139747 * A279214 A264716 A264713

Adjacent sequences: A230130 A230131 A230132 * A230134 A230135 A230136

Keyword

nonn

Author

Alois P. Heinz, Oct 10 2013

Status

approved