A230132 Number of permutations of order n with the length of longest run equal 9.

2, 36, 574, 9024, 145080, 2419872, 42129360, 767370240, 14631376500, 291914163322, 6088804487138, 132624737931726, 3012939864521998, 71296697740927172, 1755099895042102380, 44889002698811118240, 1191389820174200208622, 32774409073391657243622

Offset

9,1

Links

Alois P. Heinz, Table of n, a(n) for n = 9..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<9,
       add(g(u+j-1, o-j, t+1), j=1..o), 0))
    end:
b:= proc(u, o, t) option remember; `if`(t=9, 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=9..30);

Mathematica

length = 9;
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=9 of A211318.

A diagonal of A010026.

Sequence in context: A139738 A248343 A025608 * A141132 A064030 A367982

Adjacent sequences: A230129 A230130 A230131 * A230133 A230134 A230135

Keyword

nonn

Author

Alois P. Heinz, Oct 10 2013

Status

approved