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A079158 Sum of end-to-end Manhattan distances over all self-avoiding walks on cubic lattice trapped after n steps. 1
5, 40, 399, 2472, 17436, 98400, 601626, 3238694 (list; graph; refs; listen; history; text; internal format)
OFFSET
11,1
COMMENTS
Mean Manhattan displacement is a(n)/A077817(n).
See also "Comparison of average Euclidean and Manhattan displacements" at link
LINKS
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 self-avoiding 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 self-trapping 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: A368011 A124555 A152601 * A061633 A371372 A143437
KEYWORD
more,nonn
AUTHOR
Hugo Pfoertner, Dec 30 2002
STATUS
approved

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Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)