A358084 Sum of square end-to-end displacements over all n-step self-avoiding walks of A358036.

0, 16, 88, 288, 1104, 3264, 12032, 34144, 115112, 323888, 1043360, 2903280, 9122592, 24993552, 77246888, 209811360, 637734248, 1726546928, 5170075216, 13965402144, 41331646184, 111361083152, 326576770784, 877687158464, 2554653282056, 6850500549888, 19812687702472, 53030550412576

Offset

1,2

Comments

See A358036 for further details.

Links

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

Example

a(3) = 88 as, in the first quadrant, the three 3-step SAWs that have the first and last visited lattice point being mutually visible are:
.
                  X
                  |
     X---.        .            X
         |        |            |
     X---.    X---.    X---.---.
.
The sum of square end-to-end displacements of these three walks is 1 + 5 + 5 = 11. They can be walked in eight different ways on a square lattice thus a(3) = 11 * 8 = 88.

Crossrefs

Cf. A358036, A358083, A001411, A336448.

Sequence in context: A203249 A022676 A035291 * A309271 A120045 A301794

Adjacent sequences: A358081 A358082 A358083 * A358085 A358086 A358087

Keyword

nonn,walk

Author

Scott R. Shannon, Oct 30 2022

Status

approved