A369476 Total number of weak ascents in all length-n weak ascent sequences.

0, 1, 4, 17, 83, 461, 2873, 19846, 150418, 1240398, 11051017, 105740309, 1081101474, 11758967146, 135544030566, 1650178088102, 21155166649234, 284821038726404, 4017445572746953, 59238368957321225, 911319667593472401, 14600491369553323529, 243205500769215401307

Offset: 0

Author

Alois P. Heinz, Jan 23 2024

Keywords

• nonn

Comments

See A369321 for definitions.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..400

Crossrefs

Cf. A336070, A369321.

Programs

Maple

b:= proc(n, i, t) option remember; `if`(n=0, 1,
      add(b(n-1, j, t+`if`(j>=i, 1, 0)), j=0..t+1))
    end:
a:= n-> b(n+1, -1$2)-b(n, -1$2):
seq(a(n), n=0..23);

Formula

a(n) = Sum_{k=0..n} k * A369321(n,k).

a(n) = A336070(n+1) - A336070(n).