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Sum of square end-to-end displacements over all n-step self-avoiding walks of A358046.
1

%I #13 Nov 02 2022 07:15:42

%S 4,16,128,448,2256,5376,29424,69888,302568,741376,3026448,7216896,

%T 29268352,65785216,263892736,591065568,2279452040,5195776064,

%U 19324558176,44442289024,161417689504,371206519136,1328055630144,3044451252064,10774811055304,24625495784320,86363375773808,197092099990080

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

%C See A358046 for further details.

%e 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:

%e .

%e X

%e |

%e X---. . .---X X

%e | | | |

%e X---. X---. X---. X---.---.

%e .

%e 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.

%Y Cf. A358046, A358084, A001411, A336448.

%K nonn,walk

%O 1,1

%A _Scott R. Shannon_, Oct 30 2022