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A358084 Sum of square end-to-end displacements over all n-step self-avoiding walks of A358036.

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%I A358084 #11 Nov 02 2022 07:16:04
%S A358084 0,16,88,288,1104,3264,12032,34144,115112,323888,1043360,2903280,
%T A358084 9122592,24993552,77246888,209811360,637734248,1726546928,5170075216,
%U A358084 13965402144,41331646184,111361083152,326576770784,877687158464,2554653282056,6850500549888,19812687702472,53030550412576
%N A358084 Sum of square end-to-end displacements over all n-step self-avoiding walks of A358036.
%C A358084 See A358036 for further details.
%e A358084 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:
%e A358084 .
%e A358084                   X
%e A358084                   |
%e A358084      X---.        .            X
%e A358084          |        |            |
%e A358084      X---.    X---.    X---.---.
%e A358084 .
%e A358084 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.
%Y A358084 Cf. A358036, A358083, A001411, A336448.
%K A358084 nonn,walk
%O A358084 1,2
%A A358084 _Scott R. Shannon_, Oct 30 2022