OFFSET
1,1
COMMENTS
Fang (2020), Theorem 4.2, gives a generating function.
REFERENCES
Wenjie Fang, A partial order on Motzkin paths, Discrete Math., 343 (2020), #111802. See Section 4.
LINKS
Wenjie Fang, A partial order on Motzkin paths, arXiv preprint arXiv:1801.04809 [math.CO], 2018.
FORMULA
a(n) ~ sqrt(5/9 + 1/sqrt(3)) * (4*sqrt(45 + 26*sqrt(3))/3)^n / (sqrt(Pi)*n^(5/2)). - Vaclav Kotesovec, May 07 2020
MATHEMATICA
Rest[CoefficientList[Series[(-1 + w^4*x^2 + w*(1 + 2*x) - w^3*(3*x + 2*x^2)) / (w*x*(-1 + w^2*x)) /. w -> Root[-1 + #1 + 2*x*#1^2 - 2*x*#1^3 - x*(1 + x)*#1^4 + x^2*#1^5 &, 1], {x, 0, 30}], x]] (* Vaclav Kotesovec, May 07 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, May 07 2020
EXTENSIONS
More terms from Vaclav Kotesovec, May 07 2020
STATUS
approved