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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). 1
5, 50, 529, 3870, 40150, 185014, 1191698, 7080332 (list; graph; refs; listen; history; text; internal format)
OFFSET
11,1
LINKS
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) c 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
KEYWORD
more,nonn
AUTHOR
Hugo Pfoertner, Dec 30 2002
STATUS
approved

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Last modified July 19 00:30 EDT 2024. Contains 374388 sequences. (Running on oeis4.)