%I #26 Aug 15 2020 06:31:40

%S 1,4,12,40,118,358,936,2600,6212,16068,34936,83708,163452,357056,

%T 613592,1205716,1770616,3073480,3715920,5573480,5255048,6591160,

%U 4353912,4330096,1513712,1061392,0

%N 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 middle of the box's edge.

%F For n>=27 all terms are 0 as the walk contains more steps than there are available lattice points in the 2x2x2 box.

%e a(1) = 4 as the walk is free to move one step in four directions.

%e a(2) = 12. A first step along either edge leading to the corner leaves two possible second steps. A first step to the centre of either face can be followed by a second step to three edges or to the center of the cube, four steps in all. Thus the total number of 2-step walks is 2*2+2*4 = 12.

%e a(26) = 0 as it is not possible to visit all 26 available lattice points when the walk starts from the middle of the box's edge.

%Y Cf. A336862 (other box sizes), A337021 (start at center of box), A337033 (start at center of face), A337034 (start at corner of box), A001412, A259808, A039648.

%K nonn,walk,fini,full

%O 0,2

%A _Scott R. Shannon_, Aug 14 2020