

A079158


Sum of endtoend Manhattan distances over all selfavoiding walks on cubic lattice trapped after n steps.


1




OFFSET

11,1


COMMENTS

Mean Manhattan displacement is a(n)/A077817(n).
See also "Comparison of average Euclidean and Manhattan displacements" at link


LINKS

Table of n, a(n) for n=11..18.
Hugo Pfoertner, Results for the 3dimensional SelfTrapping Random Walk


FORMULA

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


EXAMPLE

a(12)=40 because the A077817(12)=20 trapped walks stop at 5*(1,1,0)>d=2, 5*(2,0,0)>d=2, 10*(1,0,1)>d=2. a(12)=5*2+5*2+10*2=40. See "Enumeration of all selftrapping walks of length 12" at link


PROG

FORTRAN program for distance counting available at link


CROSSREFS

Cf. A077817, A079156, A079157 (corresponding squared distance sum).
Sequence in context: A130564 A124555 A152601 * A061633 A143437 A306029
Adjacent sequences: A079155 A079156 A079157 * A079159 A079160 A079161


KEYWORD

more,nonn


AUTHOR

Hugo Pfoertner, Dec 30 2002


STATUS

approved



