A078800 Sum of end-to-end Manhattan distances over all self-avoiding walks on square lattice trapped after n steps.

1, 4, 21, 72, 271, 858, 2846, 8632, 26913, 79504, 238881, 693210, 2033133, 5823100, 16794540, 47619222, 135663289, 381615476, 1077064799, 3010363236, 8434161574, 23448994128

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..28.

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) c Program for distance counting available at link.

Crossrefs

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

Sequence in context: A212246 A359065 A095668 * A184706 A034960 A240372

Adjacent sequences: A078797 A078798 A078799 * A078801 A078802 A078803

Keyword

nonn,more

Author

Hugo Pfoertner, Dec 28 2002

Extensions

a(26)-a(28) from Sean A. Irvine, Jul 16 2025

Status

approved