

A337367


Sum of square endtoend distance over all selfavoiding nstep walks on a square lattice where no adjacent points are allowed, except those for consecutive steps.


0



0, 4, 32, 156, 608, 2116, 6816, 20844, 61376, 175628, 491248, 1349172, 3650144, 9751532, 25774672, 67501556, 175375136, 452454276, 1160098576, 2958123556, 7505767840, 18959922796, 47701159264, 119570463980, 298719578688, 743984084700, 1847709517360, 4576818079076, 11309417827072
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,2


COMMENTS

The corresponding number of nstep walks is given in A173380.


REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes the sequence A173380).


LINKS



EXAMPLE

The allowed 4step walks with their associated endtoend square distances are:
.
+ 10
4  8 8 8 16
++ + ++ + + X++++
   10  
+ + + +++ ++ + ++ 10 + 10
       
X+ X+ X+ X+ X+ X++ X++ X+++
.
The eight nonstraight walks sum to 68, and these can be walked in eight ways on the square lattice. The remaining straight walk can be walking in four ways. Thus a(4) = 68 * 8 + 16 * 4 = 608.


CROSSREFS



KEYWORD

nonn,walk


AUTHOR



STATUS

approved



