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

Author

Scott R. Shannon, Oct 30 2022

Keywords

• nonn
• walk

Comments

See A358046 for further details.

Examples

			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.