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A078800 Sum of end-to-end Manhattan distances over all self-avoiding walks on square lattice trapped after n steps. 1
1, 4, 21, 72, 271, 858, 2846, 8632, 26913, 79504, 238881, 693210, 2033133, 5823100, 16794540, 47619222, 135663289, 381615476, 1077064799 (list; graph; refs; listen; history; text; internal format)
OFFSET

7,2

COMMENTS

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

LINKS

Table of n, a(n) for n=7..25.

Hugo Pfoertner, Results for the 2D Self-Trapping Random Walk

EXAMPLE

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

PROG

FORTRAN program for distance counting available at link

CROSSREFS

Cf. A077482, A078798, A078799 (corresponding squared distance sum).

Sequence in context: A089893 A212246 A095668 * A184706 A034960 A240372

Adjacent sequences:  A078797 A078798 A078799 * A078801 A078802 A078803

KEYWORD

nonn

AUTHOR

Hugo Pfoertner, Dec 28 2002

STATUS

approved

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Last modified June 12 07:43 EDT 2021. Contains 344943 sequences. (Running on oeis4.)