A284415 Number of self-avoiding planar walks of length n starting at (0,0), ending on the x-axis, 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, 3, 5, 14, 34, 96, 259, 748, 2142, 6329, 18727, 56358, 170370, 520354, 1596980, 4935307, 15319460, 47794472, 149681904, 470620062, 1484513696, 4697619876, 14906459690, 47426014833, 151247657528, 483426998881, 1548323383749, 4968516324954, 15972198595374
Offset: 0
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..516
- Alois P. Heinz, Animation of a(6)=96 walks
- Wikipedia, Lattice path
- Wikipedia, Self-avoiding walk
Formula
a(n) = Sum_{j=floor((sqrt(1+8*n)-1)/2)..n} A284414(j,n).