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

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..555

Wikipedia, Counting lattice paths

Example

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

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);

Crossrefs

Cf. A000108, A287776.

Sequence in context: A019497 A091488 A202839 * A007561 A274295 A192676

Adjacent sequences: A371702 A371703 A371704 * A371706 A371707 A371708

Keyword

nonn

Author

Alois P. Heinz, Apr 03 2024

Status

approved