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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 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.)