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%I #6 Mar 31 2012 10:29:02
%S 5,40,399,2472,17436,98400,601626,3238694
%N Sum of end-to-end Manhattan distances over all self-avoiding walks on cubic lattice trapped after n steps.
%C Mean Manhattan displacement is a(n)/A077817(n).
%C See also "Comparison of average Euclidean and Manhattan displacements" at link
%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| + |j_l| + |k_l|) where (i_l, j_l, k_l) are the end points of all different self-avoiding walks trapped after n steps.
%e a(12)=40 because the A077817(12)=20 trapped walks stop at 5*(1,1,0)->d=2, 5*(2,0,0)->d=2, 10*(1,0,1)->d=2. a(12)=5*2+5*2+10*2=40. See "Enumeration of all self-trapping walks of length 12" at link
%o FORTRAN program for distance counting available at link
%Y Cf. A077817, A079156, A079157 (corresponding squared distance sum).
%K more,nonn
%O 11,1
%A _Hugo Pfoertner_, Dec 30 2002
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