A348010 Number of n-step self-avoiding walks on the upper half-plane of a 2D square lattice rotated by Pi/4.
1, 2, 6, 14, 40, 96, 268, 664, 1820, 4588, 12464, 31712, 85704, 219376, 590640, 1518652, 4077112, 10518364, 28177388, 72883016, 194910964, 505202708, 1349189968, 3503014492, 9344407884, 24296044256, 64748290040, 168550939272
Offset: 0
Examples
The rotated lattice, where * is the origin and + are the lattice points, is:
+ + + +
\ / \ / \ /
+ + +
/ \ / \ / \
+ + + +
\ / \ / \ /
-----+-------*-------+------
.
a(1) = 2 as the only two steps available are the diagonal steps to the northeast and northwest of the origin.
a(2) = 6 as from each of the available first steps three steps are possible, giving a total of 2 * 3 = 6 steps.
Links
- A. J. Guttmann and G. M. Torrie, Critical behavior at an edge for the SAW and Ising model, J. Phys. A 17 (1984), 3539-3552.