login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A079157 Sum of square displacements over all self-avoiding walks on cubic lattice trapped after n steps. Numerator of mean square displacement a(n)/A077817(n). 1
5, 50, 529, 3870, 40150, 185014, 1191698, 7080332 (list; graph; refs; listen; history; text; internal format)
OFFSET

11,1

LINKS

Table of n, a(n) for n=11..18.

Hugo Pfoertner, Results for the 3-dimensional Self-Trapping Random Walk

FORMULA

a(n)= sum l=1, A077817(n) (i_l^2 + j_l^2 + k_l^2) where (i_l, j_l, k_l) are the end points of all different self-avoiding walks trapped after n steps

EXAMPLE

a(12)=50 because the A077817(12)=20 trapped walks stop at 5*(1,1,0)->d^2=2, 5*(2,0,0)->d^2=4, 10*(1,0,1)->d^2=2. a(12)=5*2+5*4+10*2=50. See "Enumeration of all self-trapping walks of length 12" at link

PROG

FORTRAN program for distance counting available at link

CROSSREFS

Cf. A077817, A078605, A079158 (corresponding Manhattan distance sum).

Sequence in context: A093143 A077330 A113330 * A286974 A199762 A078244

Adjacent sequences:  A079154 A079155 A079156 * A079158 A079159 A079160

KEYWORD

more,nonn

AUTHOR

Hugo Pfoertner, Dec 30 2002

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 20 22:45 EDT 2019. Contains 326155 sequences. (Running on oeis4.)