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
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
Crossrefs
Cf. A284414.
Formula
a(n) = A284414(n,2n).