A078799 Sum of square displacements over all self-avoiding walks on square lattice trapped after n steps.
1, 6, 35, 150, 627, 2318, 8400, 28624, 96049, 311002, 994899, 3111570, 9638347, 29398762, 88985840, 266359752, 792360385, 2337329116, 6859721431, 20000471236, 58067533570, 167703151726
Offset: 7
Examples
a(9)=35 because the A077482(9)=11 different self-trapping walks stop at 5*(0,1)->d^2=1, 2*(1,2)->d^2=5, 2*(2,1)->d^2=5, (-1,0)->d^2=1 (3,0)->d^2=9. a(9)=5*1+2*5+2*5+1+9=35 See "Enumeration of all short self-trapping walks" at link
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