A316391 Number of permutations p of [n] such that the up-down signature of 0,p has nonnegative partial sums with a maximal value of four.

1, 4, 62, 340, 4734, 33855, 495371, 4403025, 70083872, 746704117, 13023762276, 161905131484, 3091115525637, 43928623624790, 914530883776894, 14623431780216366, 330413968185491070, 5870376151413374683, 143271256595612492851, 2799645366893284489691

Offset: 4

Author

Alois P. Heinz, Jul 01 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 4..455

Crossrefs

Column k=4 of A258829.

Cf. A262165, A262166.

Programs

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, 4)-b(n, 0$2, 3):
seq(a(n), n=4..23);

Formula

a(n) = A262166(n) - A262165(n).