A371705 Number of Dyck paths of semilength n such that neighboring peaks have different heights.

1, 1, 1, 3, 6, 16, 43, 116, 329, 947, 2762, 8176, 24469, 73896, 224960, 689623, 2126947, 6595273, 20548732, 64298032, 201969823, 636639087, 2013174695, 6384574754, 20302081620, 64716553655, 206764068578, 661983640080, 2123573339921, 6824597707820, 21969711674581

Offset: 0

Author

Alois P. Heinz, Apr 03 2024

Keywords

• nonn

Examples

			a(3) = 3:    /\
            /  \        /\            /\
           /    \      /  \/\      /\/  \    .
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..555
• Wikipedia, Counting lattice paths

Crossrefs

Cf. A000108, A287776.

Programs

Maple

b:= proc(x, y, h, t) option remember;
     `if`(y<0 or y>x, 0, `if`(x=0, 1, b(x-1, y+1, h, 1)+
     `if`(t=0 or y<>h, b(x-1, y-1, `if`(t=1, y, h), 0), 0)))
    end:
a:= n-> b(2*n, 0$3):
seq(a(n), n=0..30);