A079158 Sum of end-to-end Manhattan distances over all self-avoiding walks on cubic lattice trapped after n steps.
5, 40, 399, 2472, 17436, 98400, 601626, 3238694, 18355742, 96020478
Offset: 11
Examples
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.
Links
- Hugo Pfoertner, Results for the 3-dimensional Self-Trapping Random Walk
Programs
-
Fortran
c Program for distance counting available at link.
Formula
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.
Extensions
a(19)-a(20) from Sean A. Irvine, Jul 31 2025
Comments