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

0,4

Links

Table of n, a(n) for n=0..30.

Alois P. Heinz, Animation of a(6)=69 walks

Wikipedia, Lattice path

Wikipedia, Self-avoiding walk

Formula

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

Crossrefs

Cf. A000217, A284414.

Sequence in context: A070422 A102574 A317797 * A244165 A119169 A095756

Adjacent sequences: A284415 A284416 A284417 * A284419 A284420 A284421

Keyword

nonn,walk

Author

Alois P. Heinz, Mar 26 2017

Status

approved