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Search: id:A079157
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| A079157 |
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Sum of square displacements over all self-avoiding walks on cubic lattice trapped after n steps. Numerator of mean square displacement a(n)/A077817(n). |
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+0
2
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OFFSET
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11,1
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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^2 + j_l^2 + k_l^2) 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)=50 because the A077817(12)=20 trapped walks stop at 5*(1,1,0)->d^2=2, 5*(2,0,0)->d^2=4, 10*(1,0,1)->d^2=2. a(12)=5*2+5*4+10*2=50. 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, A078605, A079158 (corresponding Manhattan distance sum).
Sequence in context: A093143 A077330 A113330 this_sequence A078244 A156058 A047736
Adjacent sequences: A079154 A079155 A079156 this_sequence A079158 A079159 A079160
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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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