A079280 Number of log-concave paths of length n starting from the origin (0,0) with steps from {N=(0,1), E=(1,0) and S=(0,-1)} that stay in the second octant and never touch the line y=x except possibly at the beginning or the end.
1, 2, 2, 5, 7, 17, 26, 62, 99, 233, 382, 890, 1486, 3434, 5812, 13340, 22819, 52073, 89846, 204002, 354522, 801422, 1401292, 3155300, 5546382, 12444842, 21977516, 49155332, 87167164, 194392628, 345994216, 769547192, 1374282019, 3049104233
Offset: 1
Keywords
Formula
G.f.: (1-x)/(2-4*x) + (1+3*x)/(2*sqrt(1-4*x^2));
a(2n) = (1/2)*(4^(n-1) + 3*binomial(2n-2, n-1));
a(2n+1) = (1/2)*(2*4^(n-1) + binomial(2n, n)).
Extensions
More terms from Max Alekseyev, Jul 04 2009
Comments