A316390 Number of permutations p of [n] such that the up-down signature of 0,p has nonnegative partial sums with a maximal value of three.

1, 3, 28, 130, 1263, 8090, 88101, 724189, 8887448, 89401804, 1229179691, 14638611036, 223711095367, 3078744103979, 51892788554614, 810254535452378, 14955918856848519, 261173044555806630, 5245841953983851853, 101285541723126490941, 2201267668629421856324

Offset

3,2

Links

Alois P. Heinz, Table of n, a(n) for n = 3..458

Formula

a(n) = A262165(n) - A262164(n).

Maple

b:= proc(u, o, c, k) option remember;
      `if`(c<0 or c>k, 0, `if`(u+o=0, 1,
       add(b(u-j, o-1+j, c+1, k), j=1..u)+
       add(b(u+j-1, o-j, c-1, k), j=1..o)))
    end:
a:= n-> b(n, 0$2, 3)-b(n, 0$2, 2):
seq(a(n), n=3..23);

Crossrefs

Column k=3 of A258829.

Cf. A262164, A262165.

Sequence in context: A338791 A100019 A053132 * A048367 A095665 A145346

Adjacent sequences: A316387 A316388 A316389 * A316391 A316392 A316393

Keyword

nonn

Author

Alois P. Heinz, Jul 01 2018

Status

approved