A284428 Number of all self-avoiding planar walks of length j (0<=j<=n) starting at (0,0), ending at (n-j,0), remaining in the first quadrant and using steps (0,1), (1,0), (1,1), (-1,1), and (1,-1) with the restriction that (0,1) is never used below the diagonal and (1,0) is never used above the diagonal.
1, 0, 1, 1, 2, 1, 5, 5, 13, 15, 40, 44, 123, 156, 402, 536, 1361, 1857, 4689, 6681, 16536, 24286, 59400, 89131, 216114, 331324, 796029, 1243168, 2963859, 4700410, 11133792, 17901901, 42155014, 68618679, 160736012, 264497624, 616693942, 1024713750, 2379184108
Offset: 0
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..675
- Alois P. Heinz, Animation of a(12)=123 walks
- Wikipedia, Lattice path
- Wikipedia, Self-avoiding walk
Crossrefs
Antidiagonal sums of A284414.