A371726 Number of Dyck paths of semilength n such that neighboring peaks differ in height by at most one and first and last peak are at height one.

1, 1, 1, 1, 2, 4, 8, 17, 39, 93, 227, 567, 1447, 3760, 9917, 26492, 71567, 195256, 537397, 1490614, 4163508, 11702411, 33078992, 93986117, 268294604, 769171970, 2213834911, 6395017291, 18534987580, 53887644375, 157121564325, 459351495858, 1346290327899

Offset: 0

Author

Alois P. Heinz, Apr 04 2024

Keywords

• nonn

Examples

			a(4) = 2:                     /\
             /\/\/\/\      /\/  \/\      .
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..2031
• Alois P. Heinz, Animation of a(9)=93 paths
• Wikipedia, Counting lattice paths

Crossrefs

Cf. A000108, A287776, A371705, A371727.

Programs

Maple

b:= proc(x, y, h, t) option remember; `if`(y<0 or y>x, 0,
      `if`(x=0, `if`(h>1, 0, 1), `if`(t=1 and abs(y-h)>1, 0,
         b(x-1, y-1, `if`(t=1, y, h), 0))+b(x-1, y+1, h, 1)))
    end:
a:= n-> b(2*n, 0$3):
seq(a(n), n=0..32);