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
Keywords
Links
- 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).
Comments