%I A078798
%S A078798 6,23,80,263,834,2569,7764,23095,67910,197607,570560,1635331,4661026,
%T A078798 13212739,37296004,104836893,293710714,820132581,2283926980,6343214871,
%U A078798 17578257134,48604029143,134141458280,369519394643
%N A078798 Sum of Manhattan distances over all self-avoiding n-step walks on square 
               lattice. Numerator of mean Manhattan displacement s(n)=a(n)/A046661(n).
%C A078798 A conjectured asymptotic behavior for the mean Manhattan displacement 
               lim n-> infinity a(n)/(A046661(n)*n^(3/4))=constant is illustrated 
               in "Asymptotic Behavior of Mean Manhattan Displacement" at first 
               link
%D A078798 See under A001411
%H A078798 Hugo Pfoertner, <a href="http://www.randomwalk.de/stw2d.html">Results 
               for the 2D Self-Trapping Random Walk</a>
%F A078798 a(n)= sum k=1, A046661(n) (|i_k| + |j_k|) where (i_k, j_k) are the end 
               points of all different self-avoiding n-step walks.
%e A078798 a(3)=23 because 2 of the A046661(3)=9 walks end at Manhattan distance 
               1: (0,-1),(0,1) and 7 walks end at Manhattan distance 3: (1,-2),(1,
               2),2*(2,-1),2*(2,1),(3,0); a(3)=2*1+7*3=23 See also "Distribution 
               of end point distance" at first link
%o A078798 Source code of "FORTRAN program for distance counting" available at first 
               link
%Y A078798 Cf. A001411, A046661, A078797.
%Y A078798 Sequence in context: A058751 A034359 A114245 this_sequence A027043 A006815 
               A054491
%Y A078798 Adjacent sequences: A078795 A078796 A078797 this_sequence A078799 A078800 
               A078801
%K A078798 frac,nonn
%O A078798 2,1
%A A078798 Hugo Pfoertner (hugo(AT)pfoertner.org), Dec 10 2002