[go: up one dir, main page]

login
A371903
Total number of levels in all Dyck paths of semilength n containing exactly 2 path nodes.
1
0, 1, 3, 5, 15, 44, 134, 427, 1408, 4753, 16321, 56812, 200046, 711425, 2551886, 9222147, 33544682, 122712465, 451169747, 1666248405, 6178586630, 22994275870, 85859249486, 321562877934, 1207665205311
OFFSET
0,3
EXAMPLE
a(3) = 3 + 2 + 0 + 0 + 0 = 5:
1
_2 /\ _2 1 1
_2 / \ 3 /\/\ 3 /\ 3 /\ 3
_2 / \ _2 / \ 3 / \/\ 3 /\/ \ 4 /\/\/\ .
MAPLE
g:= proc(x, y, p) (h-> `if`(x=0, add(`if`(coeff(h, z, i)=2, 1, 0),
i=0..degree(h)), b(x, y, h)))(p+`if`(coeff(p, z, y)<3, z^y, 0))
end:
b:= proc(x, y, p) option remember; `if`(y+2<=x,
g(x-1, y+1, p), 0)+`if`(y>0, g(x-1, y-1, p), 0)
end:
a:= n-> g(2*n, 0$2):
seq(a(n), n=0..18);
CROSSREFS
Column k=2 of A371928.
Sequence in context: A103425 A119472 A018568 * A038375 A103043 A018601
KEYWORD
nonn,more
AUTHOR
Alois P. Heinz, Apr 13 2024
STATUS
approved