

A078799


Sum of square displacements over all selfavoiding walks on square lattice trapped after n steps.


1



1, 6, 35, 150, 627, 2318, 8400, 28624, 96049, 311002, 994899, 3111570, 9638347, 29398762, 88985840, 266359752, 792360385, 2337329116, 6859721431
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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..25.
Hugo Pfoertner, Results for the 2D SelfTrapping Random Walk


EXAMPLE

a(9)=35 because the A077482(9)=11 different selftrapping 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 selftrapping walks" at link


PROG

FORTRAN program for distance counting available at link


CROSSREFS

Cf. A077482, A078797, A078800 (corresponding Manhattan distance sum).
Sequence in context: A132657 A161784 A027985 * A203288 A026957 A026987
Adjacent sequences: A078796 A078797 A078798 * A078800 A078801 A078802


KEYWORD

nonn


AUTHOR

Hugo Pfoertner, Dec 26 2002


STATUS

approved



