%I #14 Aug 16 2020 14:07:58
%S 1,6,24,72,168,456,1032,2712,5784,14640,29760,71136,133344,291696,
%T 479232,950880,1343088,2375808,2774832,4266240,3909792,5046672,
%U 3230400,3316704,1122000,808128,0
%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 center of the box.
%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) = 6 as the walk is free to move one step in all six axial directions.
%e a(2) = 24 as after a step in one of the six axial directions the walk must turn along the face of the box; this eliminates the 2-step straight walk in all directions, so the total number of walks is 6*5-6 = 24.
%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.
%Y Cf. A337023 (other box sizes), A337033 (start at center of face), A335806 (start at middle of edge), A337034 (start at corner of box), A001412, A039648.
%K nonn,walk
%O 0,2
%A _Scott R. Shannon_, Aug 11 2020
|