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

4,2

Links

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

Formula

a(n) = A262166(n) - A262165(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, 4)-b(n, 0$2, 3):
seq(a(n), n=4..23);

Crossrefs

Column k=4 of A258829.

Cf. A262165, A262166.

Sequence in context: A102193 A376736 A232156 * A293968 A222791 A166028

Adjacent sequences: A316388 A316389 A316390 * A316392 A316393 A316394

Keyword

nonn

Author

Alois P. Heinz, Jul 01 2018

Status

approved