This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A078800 #11 Jul 17 2025 08:20:40 %S A078800 1,4,21,72,271,858,2846,8632,26913,79504,238881,693210,2033133, %T A078800 5823100,16794540,47619222,135663289,381615476,1077064799,3010363236, %U A078800 8434161574,23448994128 %N A078800 Sum of end-to-end Manhattan distances over all self-avoiding walks on square lattice trapped after n steps. %C A078800 The mean Manhattan displacement is given by a(n)/A077482(n) See also "Average Manhattan end point distance" and "Comparison of average Euclidean and Manhattan displacements" at link %H A078800 Hugo Pfoertner, <a href="http://www.randomwalk.de/stw2d.html">Results for the 2D Self-Trapping Random Walk</a> %e A078800 a(9)=21 because the A077482(9)=11 different self-trapping walk stop at 5*(0,1)->d=1, 2*(1,2)->d=3, 2*(2,1)->d=3,(-1,0)->d=1,(3,0)->d=3. a(9) = 5*1+2*3+2*3+1+3 = 21. %o A078800 (Fortran) c Program for distance counting available at link. %Y A078800 Cf. A077482, A078798, A078799 (corresponding squared distance sum). %K A078800 nonn,more %O A078800 7,2 %A A078800 _Hugo Pfoertner_, Dec 28 2002 %E A078800 a(26)-a(28) from _Sean A. Irvine_, Jul 16 2025