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Search: id:A079158
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| A079158 |
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Sum of end-to-end Manhattan distances over all self-avoiding walks on cubic lattice trapped after n steps. |
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+0
2
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OFFSET
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11,1
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COMMENT
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Mean Manhattan displacement is a(n)/A077817(n).
See also "Comparison of average Euclidean and Manhattan displacements" at link
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LINKS
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Hugo Pfoertner, Results for the 3-dimensional Self-Trapping Random Walk
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FORMULA
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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.
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EXAMPLE
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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
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PROGRAM
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FORTRAN program for distance counting available at link
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CROSSREFS
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Cf. A077817, A079156, A079157 (corresponding squared distance sum).
Sequence in context: A052788 A130564 A124555 this_sequence A061633 A083304 A034000
Adjacent sequences: A079155 A079156 A079157 this_sequence A079159 A079160 A079161
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KEYWORD
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more,nonn
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AUTHOR
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Hugo Pfoertner (hugo(AT)pfoertner.org), Dec 30 2002
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