A368614 Number of n-step self-avoiding walks on a 2D square lattice where each visited lattice point is either a neighbor of the first visited lattice point, else the first visited lattice point is directly visible (cf. A358036) from the lattice point when it is first visited.

4, 8, 16, 24, 48, 80, 168, 296, 624, 1144, 2424, 4552, 9680, 18480, 39368, 76128, 162376, 317288, 677624, 1335688, 2856536, 5672576, 12149080, 24280768, 52079424, 104665200, 224825088, 454047672, 976721744, 1981083216, 4267578200, 8689274768, 18743542208, 38295782400, 82715689712

Offset

1,1

Comments

The sequence counts the number of SAWs on the square lattice where, after the first step, all subsequent visited lattice points must be such that the first lattice point is directly visible from it when it is first visited - see A358036 for the definition of visibility.

Links

Table of n, a(n) for n=1..35.

Example

a(4) = 24. For walks with a second step in the first quadrant, there are three 4-step saws where the first lattice point is either a neighbor or directly visible from each point as it is first visited. These are:
.
  .---.---.   .---.     .
          |       |     |
      X---.       .     .
                  |     |
              X---.     .
                        |
                    X---.
.
where 'X' marks the position of the first lattice point. These three walks can be taken in eight ways on the 2D square lattice, so the total number of walks is 3 * 8 = 24.

Crossrefs

Cf. A358036, A358046, A001411, A337353.

Sequence in context: A140466 A343421 A337353 * A330992 A246067 A161226

Adjacent sequences: A368611 A368612 A368613 * A368615 A368616 A368617

Keyword

nonn,walk

Author

Scott R. Shannon, Dec 31 2023

Status

approved