A079157 Sum of square displacements over all self-avoiding walks on cubic lattice trapped after n steps. Numerator of mean square displacement a(n)/A077817(n).

5, 50, 529, 3870, 40150, 185014, 1191698, 7080332

Offset

11,1

Links

Table of n, a(n) for n=11..18.

Hugo Pfoertner, Results for the 3-dimensional Self-Trapping Random Walk

Formula

a(n)= sum l=1, A077817(n) (i_l^2 + j_l^2 + k_l^2) where (i_l, j_l, k_l) are the end points of all different self-avoiding walks trapped after n steps.

Example

a(12)=50 because the A077817(12)=20 trapped walks stop at 5*(1,1,0)->d^2=2, 5*(2,0,0)->d^2=4, 10*(1,0,1)->d^2=2. a(12)=5*2+5*4+10*2=50. See "Enumeration of all self-trapping walks of length 12" at link.

Prog

FORTRAN program for distance counting available at link.

Crossrefs

Cf. A077817, A078605, A079158 (corresponding Manhattan distance sum).

Sequence in context: A346937 A077330 A113330 * A286974 A199762 A078244

Adjacent sequences: A079154 A079155 A079156 * A079158 A079159 A079160

Keyword

more,nonn

Author

Hugo Pfoertner, Dec 30 2002

Status

approved