A284416 Number of self-avoiding planar walks of length 2n 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, 17, 116, 536, 3732, 21609, 152225, 991680, 7142207, 49671146, 364955208, 2644449147, 19764753353, 147264417970, 1116423286310, 8488332597668, 65109780090520, 502742629038600, 3893865922507871, 30436537169536769, 237651376621912220

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..360

Alois P. Heinz, Animation of a(5)=116 walks

Wikipedia, Lattice path

Wikipedia, Self-avoiding walk

Formula

a(n) = A284414(n,2n).

Crossrefs

Cf. A284414.

Sequence in context: A067185 A205989 A262474 * A063384 A165246 A266382

Adjacent sequences: A284413 A284414 A284415 * A284417 A284418 A284419

Keyword

nonn,walk

Author

Alois P. Heinz, Mar 26 2017

Status

approved