a(3) = 5, with 3 1's:
+----+----+----+
| 1 | 2 | 1 |
+----+----+----+
| 4 | 3 | |
+----+----+----+
| 5 | 1 | |
+----+----+----+
and
a(10) = 31, with 10 1's:
+----+----+----+----+----+----+----+----+----+----+
| | 9 | 8 | 1 | 11 | | | | | |
+----+----+----+----+----+----+----+----+----+----+
| | 1 | 7 | 6 | 10 | | | | | |
+----+----+----+----+----+----+----+----+----+----+
| 28 | 27 | 12 | 5 | 4 | 1 | | | | |
+----+----+----+----+----+----+----+----+----+----+
| 1 | 14 | 13 | 1 | 3 | 2 | 1 | | | |
+----+----+----+----+----+----+----+----+----+----+
| 16 | 15 | | | 26 | 29 | 30 | | | |
+----+----+----+----+----+----+----+----+----+----+
| 17 | 1 | 21 | 22 | 23 | 1 | 31 | | | |
+----+----+----+----+----+----+----+----+----+----+
| 18 | 19 | 20 | 1 | 24 | 25 | | | | |
+----+----+----+----+----+----+----+----+----+----+
| 1 | | | | | | | | | |
+----+----+----+----+----+----+----+----+----+----+
|