Triangle read by rows: T(n,k) is the number of weighted lattice paths in B(n) having k returns to the horizontal axis (i.e., (1,-1)-steps ending on the horizontal axis). The members of B(n) are paths of weight n that start in (0,0), end on but never go below the horizontal axis, and whose steps are of the following four kinds: a (1,0)-step with weight 1; a (1,0)-step with weight 2; a (1,1)-step with weight 2; a (1,-1)-step with weight 1. The weight of a path is the sum of the weights of its steps.

A246179

Triangle read by rows: T(n,k) is the number of weighted lattice paths in B(n) having k returns to the horizontal axis (i.e., (1,-1)-steps ending on the horizontal axis). The members of B(n) are paths of weight n that start in (0,0), end on but never go below the horizontal axis, and whose steps are of the following four kinds: a (1,0)-step with weight 1; a (1,0)-step with weight 2; a (1,1)-step with weight 2; a (1,-1)-step with weight 1. The weight of a path is the sum of the weights of its steps.