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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
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 (list; graph; refs; listen; history; text; internal format)
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 umber 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 * A240879 A056015 A128740

Adjacent sequences:  A268398 A268399 A268400 * A268402 A268403 A268404

KEYWORD

nonn

AUTHOR

Ran Pan, Feb 03 2016

STATUS

approved

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Last modified September 26 05:09 EDT 2017. Contains 292502 sequences.