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

Author

Hugo Pfoertner, Nov 27 2002

Keywords

• more
• nonn

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.

Examples

			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.
		

References

• See under A077483

Links

• Hugo Pfoertner, Results for the 2D Self-Trapping Random Walk

Crossrefs

Cf. A077483, A077484, A076874, A001411.

Programs

Fortran

c Program provided at given link

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) )