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%I #6 May 28 2024 18:29:47
%S 1,6,35,150,627,2318,8400,28624,96049,311002,994899,3111570,9638347,
%T 29398762,88985840,266359752,792360385,2337329116,6859721431
%N Sum of square displacements over all self-avoiding walks on square lattice trapped after n steps.
%C The mean squared displacement is given by a(n)/A077482(n) See also "Average Euclidean and Squared End Point Distance" at link
%H Hugo Pfoertner, <a href="http://www.randomwalk.de/stw2d.html">Results for the 2D Self-Trapping Random Walk</a>
%e a(9)=35 because the A077482(9)=11 different self-trapping walks stop at 5*(0,1)->d^2=1, 2*(1,2)->d^2=5, 2*(2,1)->d^2=5, (-1,0)->d^2=1 (3,0)->d^2=9. a(9)=5*1+2*5+2*5+1+9=35 See "Enumeration of all short self-trapping walks" at link
%o (Fortran) c Program for distance counting available at link.
%Y Cf. A077482, A078797, A078800 (corresponding Manhattan distance sum).
%K nonn
%O 7,2
%A _Hugo Pfoertner_, Dec 26 2002