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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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1
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OFFSET
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11,1
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COMMENTS
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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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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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PROG
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(Fortran) c Program for distance counting available at link.
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CROSSREFS
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KEYWORD
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more,nonn
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AUTHOR
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STATUS
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approved
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