A268430 Number of North-East paths from (0,0) to (n,n) that have even number of times bounce off y = x to the right.
1, 2, 5, 16, 53, 184, 654, 2368, 8689, 32216, 120434, 453248, 1715266, 6521584, 24894364, 95353472, 366324729, 1411015064, 5447548682, 21074836864, 81682204614, 317110750672, 1232951721604, 4800353915264, 18712880651802, 73030245143792, 285311648317172
Offset: 0
Keywords
Links
- Ran Pan, Jeffrey B. Remmel, Paired patterns in lattice paths, arXiv:1601.07988 [math.CO], 2016.
Formula
G.f.: (-1 + 3*f(x) - 2*x*(-2 + 5*f(x)+ 6*f(x)*x))/(2*(4*x - 1) (-1 + 4*x*(1 + x))), where f(x) = sqrt(1 - 4*x).
a(n) = binomial(2*n,n) - A268431(n).
Comments