I worked out on unicursal pattern on polygram and found that the sequence does not exist for distinct patterns excluded differential on orientations and reflections.
The sequence showed as following:
n unicursal pattern
3 1
4 2
5 4
6 12
7 36
8 162
9 648 Forecast from OEIS A007694
10 2592 Forecast from OEIS A007694
11 11664 Forecast from OEIS A007694
12 46656 Forecast from OEIS A007694
. . . . . . . . . . . . .
What are number of unicursal pattern for n > 8 ?