|
|
A078526
|
|
Probability P(n) of the occurrence of a 2D self-trapping walk of length n.
|
|
1
|
|
|
1, 5, 31, 173, 1521, 4224, 33418, 184183, 1370009, 3798472, 26957026, 150399317, 1034714947, 2897704261, 19494273755, 109619578524, 724456628891
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
7,2
|
|
COMMENTS
|
This is a cleaner representation than the one given by A077483 and A077484, using the upper bound for the denominator A077484 given in A076874.
|
|
REFERENCES
|
|
|
LINKS
|
|
|
FORMULA
|
P(n) = a(n) / ( 3^(n-1) * 2^(n-floor((4*n+1)^(1/2))-3) ) = a(n) / ( 3^(n-1) * 2^(A076874(n)-3) )
|
|
EXAMPLE
|
See under A077483; the inclusion of a(7)=1 is somewhat artificial due to the occurrence of 2^(-1) in the denominator: P(7)=a(7)/(3^6 *2^(7-floor(sqrt(29))-3))= 1/(729*2^(7-5-3))=1/(729*2*(-1))=2/729 See also: "Count self-trapping walks up to length 23" provided at given link.
|
|
PROG
|
FORTRAN program provided at given link
|
|
CROSSREFS
|
|
|
KEYWORD
|
more,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|