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.

5, 20, 21, 80, 92, 93, 304, 392, 408, 409, 1168, 1684, 1832, 1852, 1853, 4348, 7036, 8084, 8308, 8332, 8333, 16336, 29396, 35752, 37620, 37936, 37964, 37965, 60208, 120776, 155756, 168768, 171808, 172232, 172264, 172265, 223352, 497196, 677856, 758340, 782344, 786972, 787520, 787556, 787557

Offset: 1

Author

Scott R. Shannon, Oct 11 2020

Keywords

• nonn
• tabl

Examples

			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.
The table begins:
5;
20,21;
80,92,93;
304,392,408,409;
1168,1684,1832,1852,1853;
4348,7036,8084,8308,8332,8333;
16336,29396,35752,37620,37936,37964,37965;
60208,120776,155756,168768,171808,172232,172264,172265;
223352,497196,677856,758340,782344,786972,787520,787556,787557;
817852,2026220,2920764,3379476,3545108,3586040,3592736,3593424,3593464,3593465;
		

Links

• Scott R. Shannon, Full data table for n=1 to n=15.

Crossrefs

Cf. A338125 (start between planes), A116904 (w->infinity), A001412, A337023, A337400, A039648.

Formula

For w>=n, T(n,w) = A116904(n).