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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.
2
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
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
KEYWORD
nonn,tabl
AUTHOR
Scott R. Shannon, Oct 11 2020
STATUS
approved