Self-avoiding paths of maximum length
and minimum diameter on the hexagonal lattice
Number of segments, diameter of enclosing circle, squared radius of e.c.
3 1.1547005384 1/3
4 1.7320508076 3/4
7 2.0000000000 1
8 2.6457513111 7/4
9 2.8000000000 49/25
10 3.0000000000 9/4
12 3.0550504633 7/3
14 3.6055512755 13/4
15 3.7527767497 169/48
16 3.8157568057 91/25
19 4.0000000000 4
20 4.4388854123 133/27
22 4.5825756950 21/4
23 4.7500000000 361/64
24 4.891911267363 1729/289
25 5.003702332977 169/27
27 5.033222956847 19/3
31 5.291502622129 7
32 5.636363636364 961/121
34 5.766281297335 133/16
37 6.000000000000 9
38 6.244997998398 39/4
39 6.313411740872 21793/2187
40 6.331139971074 481/48
42 6.429100507329 31/3
43 6.661869062468 9331/841
44 6.677768533919 301/27
45 6.826571330072 3367/289
48 7.000000000000 49/4
49 7.145802963978 817/64
55 7.211102550928 13
56 7.600000000000 361/25
57 7.628073151196 931/64
58 7.741697765834 1813/121
60 7.937253933194 63/4
61 8.000000000000 16
Back to A346126.