|
|
A078800
|
|
Sum of end-to-end Manhattan distances over all self-avoiding walks on square lattice trapped after n steps.
|
|
1
|
|
|
1, 4, 21, 72, 271, 858, 2846, 8632, 26913, 79504, 238881, 693210, 2033133, 5823100, 16794540, 47619222, 135663289, 381615476, 1077064799
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
7,2
|
|
COMMENTS
|
The mean Manhattan displacement is given by a(n)/A077482(n) See also "Average Manhattan end point distance" and "Comparison of average Euclidean and Manhattan displacements" at link
|
|
LINKS
|
|
|
EXAMPLE
|
a(9)=21 because the A077482(9)=11 different self-trapping walk stop at 5*(0,1)->d=1, 2*(1,2)->d=3, 2*(2,1)->d=3,(-1,0)->d=1,(3,0)->d=3. a(9)=5*1+2*3+2*3+1+3=21
|
|
PROG
|
FORTRAN program for distance counting available at link
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|