A394180 Number of Dyck paths of semilength n such that the first peak at level y > 1 is preceded by exactly one peak at level y-1.

1, 1, 1, 2, 3, 6, 13, 30, 72, 179, 459, 1210, 3269, 9025, 25395, 72666, 211039, 621085, 1849805, 5569485, 16936433, 51976648, 160871704, 501852192, 1577115560, 4990359548, 15892383505, 50916703436, 164053673953, 531398534819, 1729937336454, 5658410545329

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..800

Wikipedia, Counting lattice paths.

Example

. a(3) = 2:                 /\
.            /\/\/\      /\/  \      ,
.
. a(4) = 3:                 /\          /\/\
.            /\/\/\/\    /\/  \/\    /\/    \    ,
.
. a(5) = 6:                                                        /\
.                           /\          /\  /\      /\/\/\      /\/  \      /\/\
.            /\/\/\/\/\  /\/  \/\/\  /\/  \/  \  /\/      \  /\/      \  /\/    \/\ .

Crossrefs

Cf. A000108, A287709.

Sequence in context: A174191 A052937 A005554 * A316766 A300660 A077212

Adjacent sequences: A394177 A394178 A394179 * A394181 A394182 A394183

Keyword

nonn

Author

Alois P. Heinz, Apr 08 2026

Status

approved