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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
See under A077483
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) c Program provided at given link
CROSSREFS
Sequence in context: A237622 A239334 A180635 * A255236 A202753 A057426
KEYWORD
more,nonn
AUTHOR
Hugo Pfoertner, Nov 27 2002
STATUS
approved

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Last modified June 22 01:41 EDT 2024. Contains 373561 sequences. (Running on oeis4.)