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

1,1

Links

Table of n, a(n) for n=1..45.

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

Formula

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

Example

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;

Crossrefs

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

Sequence in context: A101728 A053240 A034123 * A360368 A088973 A005240

Adjacent sequences: A338123 A338124 A338125 * A338127 A338128 A338129

Keyword

nonn,tabl

Author

Scott R. Shannon, Oct 11 2020

Status

approved