Number of weighted lattice paths in L_n having no peaks. 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. A peak is a (1,1)-step followed by a (1,-1)-step.
A182904
Number of weighted lattice paths in L_n having no peaks. 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. A peak is a (1,1)-step followed by a (1,-1)-step.
Terms
- a(0) =1a(1) =1a(2) =2a(3) =4a(4) =9a(5) =21a(6) =48a(7) =112a(8) =263a(9) =623a(10) =1484a(11) =3550a(12) =8525a(13) =20537a(14) =49612a(15) =120136a(16) =291519a(17) =708699a(18) =1725714a(19) =4208364a(20) =10276173a(21) =25122829a(22) =61486180a(23) =150632012a(24) =369361757a(25) =906462529a(26) =2226297008a(27) =5471757126a(28) =13457326605a(29) =33117622245
External references
- oeis: A182904