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 A079158 #20 Aug 01 2025 11:08:44
%S A079158 5,40,399,2472,17436,98400,601626,3238694,18355742,96020478
%N A079158 Sum of end-to-end Manhattan distances over all self-avoiding walks on cubic lattice trapped after n steps.
%C A079158 Mean Manhattan displacement is a(n)/A077817(n).
%C A079158 See also "Comparison of average Euclidean and Manhattan displacements" at link
%H A079158 Hugo Pfoertner, <a href="https://www.randomwalk.de/stw3d.html">Results for the 3-dimensional Self-Trapping Random Walk</a>
%F A079158 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 A079158 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, so a(12)=5*2+5*2+10*2=40. See "Enumeration of all self-trapping walks of length 12" at link.
%o A079158 (Fortran) c Program for distance counting available at link.
%Y A079158 Cf. A077817, A079156, A079157 (corresponding squared distance sum).
%K A079158 more,nonn
%O A079158 11,1
%A A079158 _Hugo Pfoertner_, Dec 30 2002
%E A079158 a(19)-a(20) from _Sean A. Irvine_, Jul 31 2025