41345

Appears in sequences

• Triangle, read by rows, defined by T(n,k) = T(n-1,k) + T(n,k-1) for nk>0, where T(n,0) = T(n-1,0) + T(n-1,n-1) and T(n,n) = T(n,n-1) for n>0 with T(0,0)=1.at n=45A129577
• Column 0 of triangle A129577.at n=9A129578
• Triangle read by rows: T(n,k) is the number of weighted lattice paths in L_n having k (1,0)-steps of weight 2 at level 0. The members of L_n are paths of weight n that start at (0,0) , end on the horizontal axis and whose steps are of the following four kinds: an (1,0)-step with weight 1, an (1,0)-step with weight 2, a (1,1)-step with weight 2, and a (1,-1)-step with weight 1. The weight of a path is the sum of the weights of its steps.at n=56A182891
• Number of weighted lattice paths in L_n having no (1,0)-steps of weight 2 at level 0.at n=14A182892
• Number of ordered triples (w,x,y) with all terms in {1,...,n} and w^4<x^4+y^4.at n=39A211652