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

Author

Scott R. Shannon, Oct 30 2022

Keywords

• nonn
• walk

Comments

See A358036 for further details.

Examples

			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.