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Search: id:A078799
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| A078799 |
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Sum of square displacements over all self-avoiding walks on square lattice trapped after n steps. |
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+0
2
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| 1, 6, 35, 150, 627, 2318, 8400, 28624, 96049, 311002, 994899, 3111570, 9638347, 29398762, 88985840, 266359752, 792360385, 2337329116, 6859721431
(list; graph; listen)
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OFFSET
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7,2
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COMMENT
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The mean squared displacement is given by a(n)/A077482(n) See also "Average Euclidean and Squared End Point Distance" at link
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LINKS
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Hugo Pfoertner, Results for the 2D Self-Trapping Random Walk
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EXAMPLE
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a(9)=35 because the A077482(9)=11 different self-trapping walks stop at 5*(0,1)->d^2=1, 2*(1,2)->d^2=5, 2*(2,1)->d^2=5, (-1,0)->d^2=1 (3,0)->d^2=9. a(9)=5*1+2*5+2*5+1+9=35 See "Enumeration of all short self-trapping walks" 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. A077482, A078797, A078800 (corresponding Manhattan distance sum).
Adjacent sequences: A078796 A078797 A078798 this_sequence A078800 A078801 A078802
Sequence in context: A089581 A132657 A027985 this_sequence A026957 A026987 A030532
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KEYWORD
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nonn
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AUTHOR
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Hugo Pfoertner (hugo(AT)pfoertner.org), Dec 26 2002
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