Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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