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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

Table of n, a(n) for n=11..18.

Hugo Pfoertner, Results for the 3-dimensional Self-Trapping 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 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: 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

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Last modified December 15 00:30 EST 2019. Contains 329988 sequences. (Running on oeis4.)