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

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: A081113 A368429 A114587 * A033114 A096881 A363588

Adjacent sequences: A268428 A268429 A268430 * A268432 A268433 A268434

Keyword

nonn

Author

Ran Pan, Feb 04 2016

Status

approved