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A078799 Sum of square displacements over all self-avoiding walks on square lattice trapped after n steps. 1
1, 6, 35, 150, 627, 2318, 8400, 28624, 96049, 311002, 994899, 3111570, 9638347, 29398762, 88985840, 266359752, 792360385, 2337329116, 6859721431 (list; graph; refs; listen; history; text; internal format)
OFFSET

7,2

COMMENTS

The mean squared displacement is given by a(n)/A077482(n) See also "Average Euclidean and Squared End Point Distance" 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)=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

PROG

FORTRAN program for distance counting available at link

CROSSREFS

Cf. A077482, A078797, A078800 (corresponding Manhattan distance sum).

Sequence in context: A132657 A161784 A027985 * A203288 A026957 A026987

Adjacent sequences:  A078796 A078797 A078798 * A078800 A078801 A078802

KEYWORD

nonn

AUTHOR

Hugo Pfoertner, Dec 26 2002

STATUS

approved

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Last modified November 13 00:25 EST 2019. Contains 329083 sequences. (Running on oeis4.)