Number of (1,-1)-returns to the horizontal axis in all weighted lattice paths in L_n. 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.
A182897
Number of (1,-1)-returns to the horizontal axis in all weighted lattice paths in L_n. 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.
Terms
- a(0) =0a(1) =0a(2) =0a(3) =1a(4) =3a(5) =9a(6) =27a(7) =76a(8) =211a(9) =580a(10) =1578a(11) =4267a(12) =11484a(13) =30789a(14) =82301a(15) =219465a(16) =584060a(17) =1551770a(18) =4117061a(19) =10910049a(20) =28881387a(21) =76387179a(22) =201875129a(23) =533145603a(24) =1407161007a(25) =3711981168a(26) =9787157469a(27) =25793933410a(28) =67952779665a(29) =178954077522
External references
- oeis: A182897