OFFSET
4,2
COMMENTS
This sequence is related to paired pattern P_2 in Pan and Remmel's link.
By symmetry, it is also the number of North-East lattice paths from (0,0) to (n,n) that bounce off the diagonal y = x to the left exactly three times.
LINKS
Ran Pan and Jeffrey B. Remmel, Paired patterns in lattice paths, arXiv:1601.07988 [math.CO], 2016.
FORMULA
G.f.: -((-1 + f(x))^4*x^2*(-1 + f(x) + 2*x))/(2*(1 - f(x) + (-5 + f(x))*x)^4), where f(x) = sqrt(1 - 4*x).
CROSSREFS
KEYWORD
nonn
AUTHOR
Ran Pan, Feb 03 2016
STATUS
approved