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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 Table of n, a(n) for n=7..23. Hugo Pfoertner, Results for the 2D Self-Trapping Random Walk 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 Cf. A077483, A077484, A076874, A001411. Sequence in context: A237622 A239334 A180635 * A255236 A202753 A057426 Adjacent sequences: A078523 A078524 A078525 * A078527 A078528 A078529 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.)