A358083 Sum of square end-to-end displacements over all n-step self-avoiding walks of A358046.

4, 16, 128, 448, 2256, 5376, 29424, 69888, 302568, 741376, 3026448, 7216896, 29268352, 65785216, 263892736, 591065568, 2279452040, 5195776064, 19324558176, 44442289024, 161417689504, 371206519136, 1328055630144, 3044451252064, 10774811055304, 24625495784320, 86363375773808, 197092099990080

Offset

1,1

Comments

See A358046 for further details.

Links

Table of n, a(n) for n=1..28.

Example

a(3) = 128 as, in the first quadrant, the four 3-step SAWs that have the first and last visited lattice point being mutually visible are:
.
                  X
                  |
     X---.        .          .---X           X
         |        |          |               |
     X---.    X---.      X---.       X---.---.
.
The sum of square end-to-end displacements of these four walks is 1 + 5 + 5 + 5 = 16. They can be walked in eight different ways on a square lattice thus a(3) = 16 * 8 = 128.

Crossrefs

Cf. A358046, A358084, A001411, A336448.

Sequence in context: A094356 A322236 A318152 * A323552 A363443 A349264

Adjacent sequences: A358080 A358081 A358082 * A358084 A358085 A358086

Keyword

nonn,walk

Author

Scott R. Shannon, Oct 30 2022

Status

approved