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 A078798 #13 Jul 16 2025 21:55:52
%S A078798 1,6,23,80,263,834,2569,7764,23095,67910,197607,570560,1635331,
%T A078798 4661026,13212739,37296004,104836893,293710714,820132581,2283926980,
%U A078798 6343214871,17578257134,48604029143,134141458280,369519394643
%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 (Fortran) c Source code of "FORTRAN program for distance counting" available at first link.
%Y A078798 Cf. A001411, A046661, A078797.
%K A078798 frac,nonn
%O A078798 1,2
%A A078798 _Hugo Pfoertner_, Dec 10 2002
%E A078798 a(1)=1 inserted by _Sean A. Irvine_, Jul 16 2025