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A358083 Sum of square end-to-end displacements over all n-step self-avoiding walks of A358046.

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%I A358083 #13 Nov 02 2022 07:15:42
%S A358083 4,16,128,448,2256,5376,29424,69888,302568,741376,3026448,7216896,
%T A358083 29268352,65785216,263892736,591065568,2279452040,5195776064,
%U A358083 19324558176,44442289024,161417689504,371206519136,1328055630144,3044451252064,10774811055304,24625495784320,86363375773808,197092099990080
%N A358083 Sum of square end-to-end displacements over all n-step self-avoiding walks of A358046.
%C A358083 See A358046 for further details.
%e A358083 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 A358083 .
%e A358083                   X
%e A358083                   |
%e A358083      X---.        .          .---X           X
%e A358083          |        |          |               |
%e A358083      X---.    X---.      X---.       X---.---.
%e A358083 .
%e A358083 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 A358083 Cf. A358046, A358084, A001411, A336448.
%K A358083 nonn,walk
%O A358083 1,1
%A A358083 _Scott R. Shannon_, Oct 30 2022