A268401 Number of North-East lattice paths from (0,0) to (n,n) that bounce off the diagonal y = x to the right exactly three times.

1, 6, 31, 146, 655, 2850, 12148, 51028, 212039, 873870, 3578404, 14578576, 59149381, 239177006, 964439355, 3879856458, 15577609711, 62439489346, 249917575553, 999080441830, 3989726087031, 15917901326330, 63457122234055, 252796365476922, 1006456231070795, 4004838954237250, 15928299669867291

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

Table of n, a(n) for n=4..30.

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

Cf. A268400.

Sequence in context: A094951 A099621 A291002 * A346226 A240879 A056015

Adjacent sequences: A268398 A268399 A268400 * A268402 A268403 A268404

Keyword

nonn

Author

Ran Pan, Feb 03 2016

Status

approved