A078526 - OEIS

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A078526

Probability P(n) of the occurrence of a 2D self-trapping walk of length n.

1, 5, 31, 173, 1521, 4224, 33418, 184183, 1370009, 3798472, 26957026, 150399317, 1034714947, 2897704261, 19494273755, 109619578524, 724456628891 (list; graph; refs; listen; history; 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	`Hugo Pfoertner, Results for the 2D Self-Trapping Random Walk`
	FORMULA	`P(n) = a(n) / ( 3^(n-1) * 2^(n-floor((4n+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/(7292^(7-5-3))=1/(7292(-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	`Cf. A077483, A077484, A076874, A001411.` `Sequence in context: A045904 A034353 A180635 * A137626 A202753 A057426` `Adjacent sequences: A078523 A078524 A078525 * A078527 A078528 A078529`
	KEYWORD	`more,nonn`
	AUTHOR	`Hugo Pfoertner (hugo(AT)pfoertner.org), Nov 27 2002`

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Last modified February 17 08:21 EST 2012. Contains 205998 sequences.