A394180 - OEIS

%I #35 Apr 11 2026 18:14:09

%S 1,1,1,2,3,6,13,30,72,179,459,1210,3269,9025,25395,72666,211039,

%T 621085,1849805,5569485,16936433,51976648,160871704,501852192,

%U 1577115560,4990359548,15892383505,50916703436,164053673953,531398534819,1729937336454,5658410545329

%N 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.

%H Alois P. Heinz, <a href="/A394180/b394180.txt">Table of n, a(n) for n = 0..800</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Lattice_path#Counting_lattice_paths">Counting lattice paths</a>.

%e . a(3) = 2:                 /\

%e .            /\/\/\      /\/  \      ,

%e .

%e . a(4) = 3:                 /\          /\/\

%e .            /\/\/\/\    /\/  \/\    /\/    \    ,

%e .

%e . a(5) = 6:                                                        /\

%e .                           /\          /\  /\      /\/\/\      /\/  \      /\/\

%e .            /\/\/\/\/\  /\/  \/\/\  /\/  \/  \  /\/      \  /\/      \  /\/    \/\ .

%Y Cf. A000108, A287709.

%K nonn

%O 0,4

%A _Alois P. Heinz_, Apr 08 2026