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

0,5

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

Example

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

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);

Crossrefs

Cf. A000108, A287776, A371705, A371727.

Sequence in context: A000598 A003008 A185352 * A054199 A054197 A287776

Adjacent sequences: A371723 A371724 A371725 * A371727 A371728 A371729

Keyword

nonn

Author

Alois P. Heinz, Apr 04 2024

Status

approved