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

0,3

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).

Crossrefs

Column sums of A284414.

Cf. A001006, A003056.

Sequence in context: A271867 A295064 A052974 * A318227 A363542 A230585

Adjacent sequences: A284412 A284413 A284414 * A284416 A284417 A284418

Keyword

nonn,walk

Author

Alois P. Heinz, Mar 26 2017

Status

approved