A284428 Number of all self-avoiding planar walks of length j (0<=j<=n) starting at (0,0), ending at (n-j,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, 0, 1, 1, 2, 1, 5, 5, 13, 15, 40, 44, 123, 156, 402, 536, 1361, 1857, 4689, 6681, 16536, 24286, 59400, 89131, 216114, 331324, 796029, 1243168, 2963859, 4700410, 11133792, 17901901, 42155014, 68618679, 160736012, 264497624, 616693942, 1024713750, 2379184108

Offset

0,5

Links

Alois P. Heinz, Table of n, a(n) for n = 0..675

Alois P. Heinz, Animation of a(12)=123 walks

Wikipedia, Lattice path

Wikipedia, Self-avoiding walk

Crossrefs

Antidiagonal sums of A284414.

Sequence in context: A377806 A167158 A074392 * A096976 A052547 A119245

Adjacent sequences: A284425 A284426 A284427 * A284429 A284430 A284431

Keyword

nonn,walk

Author

Alois P. Heinz, Mar 26 2017

Status

approved