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

7,2

Comments

The mean squared displacement is given by a(n)/A077482(n) See also "Average Euclidean and Squared End Point Distance" at link

Links

Table of n, a(n) for n=7..28.

Hugo Pfoertner, Results for the 2D Self-Trapping Random Walk

Example

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

Prog

(Fortran) c Program for distance counting available at link.

Crossrefs

Cf. A077482, A078797, A078800 (corresponding Manhattan distance sum).

Sequence in context: A379628 A161784 A027985 * A203288 A026957 A026987

Adjacent sequences: A078796 A078797 A078798 * A078800 A078801 A078802

Keyword

nonn,more

Author

Hugo Pfoertner, Dec 26 2002

Extensions

a(26)-a(28) from Sean A. Irvine, Jul 16 2025

Status

approved