A316393 Number of permutations p of [n] such that the up-down signature of 0,p has nonnegative partial sums with a maximal value of six.

1, 6, 261, 1890, 52022, 455231, 11174035, 116105272, 2810232512, 34036483163, 844691910962, 11731978216291, 303637667232802, 4769379288424677, 129700918311614279, 2277005590881369266, 65261900211279910831, 1267764017301809851710, 38324737795523150842616

Offset

6,2

Links

Alois P. Heinz, Table of n, a(n) for n = 6..452

Formula

a(n) = A262168(n) - A262167(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, 6)-b(n, 0$2, 5):
seq(a(n), n=6..24);

Crossrefs

Column k=6 of A258829.

Cf. A262167, A262168.

Sequence in context: A015020 A225166 A003384 * A366226 A332126 A229579

Adjacent sequences: A316390 A316391 A316392 * A316394 A316395 A316396

Keyword

nonn

Author

Alois P. Heinz, Jul 01 2018

Status

approved