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%I #8 Dec 26 2023 16:53:29
%S 5,50,529,3870,40150,185014,1191698,7080332
%N Sum of square displacements over all self-avoiding walks on cubic lattice trapped after n steps. Numerator of mean square displacement a(n)/A077817(n).
%H Hugo Pfoertner, <a href="http://www.randomwalk.de/stw3d.html">Results for the 3-dimensional Self-Trapping Random Walk</a>
%F a(n)= sum l=1, A077817(n) (i_l^2 + j_l^2 + k_l^2) where (i_l, j_l, k_l) are the end points of all different self-avoiding walks trapped after n steps.
%e a(12)=50 because the A077817(12)=20 trapped walks stop at 5*(1,1,0)->d^2=2, 5*(2,0,0)->d^2=4, 10*(1,0,1)->d^2=2. a(12)=5*2+5*4+10*2=50. See "Enumeration of all self-trapping walks of length 12" at link.
%o FORTRAN program for distance counting available at link.
%Y Cf. A077817, A078605, A079158 (corresponding Manhattan distance sum).
%K more,nonn
%O 11,1
%A _Hugo Pfoertner_, Dec 30 2002
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