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

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