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Search: id:A078800
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| A078800 |
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Sum of end-to-end Manhattan distances over all self-avoiding walks on square lattice trapped after n steps. |
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+0
2
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| 1, 4, 21, 72, 271, 858, 2846, 8632, 26913, 79504, 238881, 693210, 2033133, 5823100, 16794540, 47619222, 135663289, 381615476, 1077064799
(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 Manhattan displacement is given by a(n)/A077482(n) See also "Average Manhattan end point distance" and "Comparison of average Euclidean and Manhattan displacements" 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)=21 because the A077482(9)=11 different self-trapping walk stop at 5*(0,1)->d=1, 2*(1,2)->d=3, 2*(2,1)->d=3,(-1,0)->d=1,(3,0)->d=3. a(9)=5*1+2*3+2*3+1+3=21
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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, A078798, A078799 (corresponding squared distance sum).
Sequence in context: A131478 A089893 A095668 this_sequence A057333 A034960 A157493
Adjacent sequences: A078797 A078798 A078799 this_sequence A078801 A078802 A078803
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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 28 2002
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