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A338126 Triangle read by rows: T(n,w) is the number of n-step self avoiding walks on a 3D cubic lattice confined between two infinite planes a distance w apart where the walk starts on one of the planes.

%I A338126 #13 Oct 14 2020 23:16:32
%S A338126 5,20,21,80,92,93,304,392,408,409,1168,1684,1832,1852,1853,4348,7036,
%T A338126 8084,8308,8332,8333,16336,29396,35752,37620,37936,37964,37965,60208,
%U A338126 120776,155756,168768,171808,172232,172264,172265,223352,497196,677856,758340,782344,786972,787520,787556,787557
%N A338126 Triangle read by rows: T(n,w) is the number of n-step self avoiding walks on a 3D cubic lattice confined between two infinite planes a distance w apart where the walk starts on one of the planes.
%H A338126 Scott R. Shannon, <a href="/A338126/a338126_1.txt">Full data table for n=1 to n=15</a>.
%F A338126 For w>=n, T(n,w) = A116904(n).
%e A338126 T(2,1) = 20 as after one step towards the opposite plane the walk must turn along that plane; this eliminates the 2-step straight walk in that direction, so the total number of walks is A116904(2) - 1 = 21 - 1 = 20.
%e A338126 The table begins:
%e A338126 5;
%e A338126 20,21;
%e A338126 80,92,93;
%e A338126 304,392,408,409;
%e A338126 1168,1684,1832,1852,1853;
%e A338126 4348,7036,8084,8308,8332,8333;
%e A338126 16336,29396,35752,37620,37936,37964,37965;
%e A338126 60208,120776,155756,168768,171808,172232,172264,172265;
%e A338126 223352,497196,677856,758340,782344,786972,787520,787556,787557;
%e A338126 817852,2026220,2920764,3379476,3545108,3586040,3592736,3593424,3593464,3593465;
%Y A338126 Cf. A338125 (start between planes), A116904 (w->infinity), A001412, A337023, A337400, A039648.
%K A338126 nonn,tabl
%O A338126 1,1
%A A338126 _Scott R. Shannon_, Oct 11 2020