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A268431 Number of North-East 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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 26 06:54 EDT 2017. Contains 292502 sequences.