cp's OEIS Frontend

A337033 The number of n-step self avoiding walks on a 3D cubic lattice confined inside a box of size 2x2x2 where the walk starts at the center of one of the box's faces.

%I A337033 #11 Aug 16 2020 13:55:48
%S A337033 1,5,17,52,148,400,1060,2700,6720,15760,36248,77856,163296,312760,
%T A337033 590536,995160,1663664,2405056,3482320,4180656,5080320,4823560,
%U A337033 4686432,3165088,2228584,792272,303264,0
%N A337033 The number of n-step self avoiding walks on a 3D cubic lattice confined inside a box of size 2x2x2 where the walk starts at the center of one of the box's faces.
%F A337033 For n>=27 all terms are 0 as the walk contains more steps than there are available lattice points in the 2x2x2 box.
%e A337033 a(1) = 5 as the walk is free to move one step in five possible directions. It cannot take a step to a direction opposite to the face's normal it starts on.
%e A337033 a(2) = 17. Taking the first along the starting face hits the box's edge after which the walks has three directions for the second step, giving 4*3 = 12 walks in all. A first step away from the starting face can be followed by a second step in five directions. The total number of 2-step walks is therefore 12+5 = 17.
%e A337033 a(26) = 303264. This is the total number of ways a 26-step walk can completely fill the 2x2x2 box's 26 available lattice points. Unlike the walk which starts at the center of the box, see A337021, all lattice points can be visited in one walk.
%Y A337033 Cf. A337031 (other box sizes), A337021 (start at center of box), A335806 (start at middle of edge), A337034 (start at corner of box),  A001412, A116904.
%K A337033 nonn,walk,fini,full
%O A337033 0,2
%A A337033 _Scott R. Shannon_, Aug 12 2020