login
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.
2
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
0,9
LINKS
EXAMPLE
a(7) = 1: /\
/\/ \/\
/\/ \/\
a(8) = 2: /\ /\
/\/ \ /\ /\ / \/\
/\/ \/ \/\ /\/ \/ \/\
a(9) = 1: /\
/\ / \ /\
/\/ \/ \/ \/\
a(10) = 1: /\
/\/ \/\
/\/ \/\
/\/ \/\ .
MAPLE
b:= proc(x, y, v) option remember; (t-> `if`(x=t, 1,
`if`(x<t, 0, add(b(x-1-2*i, y-1, 0), i=1..y-1)+
`if`(v=1, add(b(x-1-2*i, y+1, v), i=1..y), 0))))(3*y-2)
end:
a:= n-> `if`(n=0, 1, b(2*n-1, 1$2)):
seq(a(n), n=0..50);
CROSSREFS
Sequence in context: A096540 A277081 A111569 * A213786 A055130 A051292
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Apr 12 2024
STATUS
approved