A078800 Sum of end-to-end Manhattan distances over all self-avoiding walks on square lattice trapped after n steps.
1, 4, 21, 72, 271, 858, 2846, 8632, 26913, 79504, 238881, 693210, 2033133, 5823100, 16794540, 47619222, 135663289, 381615476, 1077064799, 3010363236, 8434161574, 23448994128
Offset: 7
Examples
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.
Links
- Hugo Pfoertner, Results for the 2D Self-Trapping Random Walk
Programs
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Fortran
c Program for distance counting available at link.
Extensions
a(26)-a(28) from Sean A. Irvine, Jul 16 2025
Comments