

A268431


Number of NorthEast paths from (0,0) to (n,n) that have odd number of times bounce off y = x to the right.


1



1, 4, 17, 68, 270, 1064, 4181, 16404, 64322, 252184, 988890, 3879016, 15222236, 59764048, 234755661, 922591156, 3627586618, 14270426936, 56164324206, 221147123768, 871147242116, 3433076812336, 13534723031298, 53380361293960, 210606884630932
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OFFSET

2,2


COMMENTS

This sequence is related to paired pattern P_2 in Section 3.2 in Pan and Remmel's link.


LINKS

Table of n, a(n) for n=2..26.
Ran Pan, Jeffrey B. Remmel, Paired patterns in lattice paths, arXiv:1601.07988 [math.CO], 2016.


FORMULA

a(n) = binomial(2*n,n)  A268430(n).
G.f.: (2*x^2)/(1 + f(x)  2*x*(2 + f(x) + 2*f(x)*x)), where f(x) = sqrt(1  4*x).


CROSSREFS

Cf. A268407, A268429, A268430.
Sequence in context: A239845 A081113 A114587 * A033114 A096881 A033122
Adjacent sequences: A268428 A268429 A268430 * A268432 A268433 A268434


KEYWORD

nonn


AUTHOR

Ran Pan, Feb 04 2016


STATUS

approved



