A284418 Number of self-avoiding planar walks of length n*(n+1)/2 starting at (0,0), ending at (n,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, 1, 1, 7, 10, 31, 69, 196, 451, 1168, 2813, 7119, 17618, 44206, 111399, 277972, 709411, 1763795, 4543873, 11269489, 29244239, 72402587, 188977618, 467258134, 1225383748, 3026799348, 7969173506, 19669004793, 51959167749, 128161003199, 339530403506

Offset: 0

Author

Alois P. Heinz, Mar 26 2017

Keywords

• nonn
• walk

Links

• Alois P. Heinz, Animation of a(6)=69 walks
• Wikipedia, Lattice path
• Wikipedia, Self-avoiding walk

Crossrefs

Cf. A000217, A284414.

Formula

a(n) = A284414(n,n*(n+1)/2).