A078526 - OEIS

%I #6 May 27 2024 11:36:13

%S 1,5,31,173,1521,4224,33418,184183,1370009,3798472,26957026,150399317,

%T 1034714947,2897704261,19494273755,109619578524,724456628891

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

%C This is a cleaner representation than the one given by A077483 and A077484, using the upper bound for the denominator A077484 given in A076874.

%D See under A077483

%H Hugo Pfoertner, <a href="http://www.randomwalk.de/stw2d.html">Results for the 2D Self-Trapping Random Walk</a>

%F 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) )

%e 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.

%o (Fortran) c Program provided at given link

%Y Cf. A077483, A077484, A076874, A001411.

%K more,nonn

%O 7,2

%A _Hugo Pfoertner_, Nov 27 2002