A371926 Number of Dyck paths of semilength n with strongly unimodal peak heights such that neighboring peaks differ in height by exactly one and first and last peak are at height one.

1, 1, 0, 0, 1, 0, 0, 1, 2, 1, 1, 4, 8, 11, 14, 23, 44, 79, 130, 209, 347, 598, 1042, 1801, 3084, 5273, 9060, 15658, 27152, 47122, 81769, 141919, 246525, 428742, 746479, 1300806, 2268169, 3956840, 6905817, 12057999, 21063319, 36809385, 64350631, 112535774

Offset: 0

Author

Alois P. Heinz, Apr 12 2024

Keywords

• nonn

Examples

			a(7) = 1:           /\
                 /\/  \/\
              /\/        \/\
a(8) = 2:           /\                      /\
                 /\/  \  /\            /\  /  \/\
              /\/      \/  \/\      /\/  \/      \/\
a(9) = 1:           /\
               /\  /  \  /\
            /\/  \/    \/  \/\
a(10) = 1:          /\
                 /\/  \/\
              /\/        \/\
           /\/              \/\     .
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..2500
• Wikipedia, Counting lattice paths

Crossrefs

Cf. A000108, A371727.

Programs

Maple

b:= proc(x, y, v) option remember; (t-> `if`(x=t, 1,
     `if`(x `if`(n=0, 1, b(2*n-1, 1$2)):
seq(a(n), n=0..50);