%I #28 May 27 2024 11:45:32
%S 1,2,11,25,95,228,752,1860,5741,14477,42939,109758,317147,818229,
%T 2322512,6030293,16900541,44079555,122379267,320227677,882687730,
%U 2315257359,6346076015,16675422679,45502168379,119728011251,325510252108,857400725204
%N Number of self-avoiding walks on square lattice trapped after n steps.
%C Only 1/8 of all possible walks is counted by selecting the first step in +x direction and requiring the first step changing y to be positive.
%D See references given for A001411.
%H Hugo Pfoertner, <a href="https://www.randomwalk.de/stw2d.html">Results for the 2D Self-Trapping Random Walk</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Self-AvoidingWalk.html">Self-Avoiding Walk.</a>
%e a(7) = 1 because there is only 1 self-trapping walk with 7 steps: (0,0)(1,0)(1,1)(1,2)(0,2)(-1,2)(-1,1)(0,1); a(8) = 2 because there are 2 self-trapping walks with 8 steps: (0,0)(1,0)(2,0)(2,1)(2,2)(1,2)(0,2)(0,1)(1,1) and (0,0)(1,0)(1,1)(2,1)(3,1)(3,0)(3,-1)(2,-1)(2,0).
%o (Fortran) c Program provided at given link.
%Y Cf. A001411, A046661, A174517, A322831.
%K more,nonn,walk
%O 7,2
%A _Hugo Pfoertner_, Nov 07 2002
%E a(26)-a(28) from _Alois P. Heinz_, Jun 16 2011
%E a(29)-a(34) from _Bert Dobbelaere_, Jan 03 2019
|