Tables of Solutions
OEIS.org numbers are given in the table heading.
A dash (-) in the table means that no solutions are possible for the value of n. Question marks '?' denote unsolved values.
OEIS.org numbers are given in the table heading.
A dash (-) in the table means that no solutions are possible for the value of n. Question marks '?' denote unsolved values.
Conditions for solvability:
11
and 111
are the trivial solutions for V(2,1) and V(3,1).
| n | Pairs L(2,n) |
Pairs V(2,n) |
Triplets L(3,n) |
Triplets V(3,n) |
Quads L(4,n) |
|---|---|---|---|---|---|
| A014552 | A059106 | no oeis | no oeis | no | |
| 1 | - | 1 | - | 1 | - |
| 2 | - | - | - | - | - |
| 3 | 1 | - | - | - | - |
| 4 | 1 | 3 | - | - | - |
| 5 | - | 5 | - | - | - |
| 6 | - | - | - | - | - |
| 7 | 26 | - | - | - | - |
| 8 | 150 | 252 | * | - | - |
| 9 | - | 1,328 | 3 | 9 | - |
| 10 | - | - | 5 | 20 | - |
| 11 | 17,792 | - | - | 33 | - |
| 12 | 108,144 | 227,968 | - | - | - |
| 13 | - | 1,520,280 | - | - | - |
| 14 | - | - | - | - | - |
| 15 | 39,809,640 | - | - | - | - |
| 16 | 326,721,800 | 700,078,384 | - | - | - |
| 17 | - | 6,124,491,248 | 13,440 | - | - |
| 18 | - | - | 54,947 | 200,343 | - |
| 19 | 256,814,891,280 | - | 249,280 | 869,006 | - |
| 20 | 2,636,337,861,200 | 5,717,789,399,488 | - | 4,247,790 | - |
| 21 | - | 61,782,464,083,584 | - | - | - |
| 22 | - | - | - | - | - |
| 23 | 3,799,455,942,515,488 | - | - | - | - |
| 24 | 46,845,158,056,515,936 | ?? | - | - | 3 |
| 25 | - | ?? | - | - | - |
| 26 | - | - | ??? | - | - |
| 27 | 111,683,611,098,764,903,232 | - | ??? | ??? | - |
| 28 | 1,607,383,260,609,382,393,152 | ?? | ??? | ??? | - |
| 29 | - | ?? | - | ??? | - |
| 30 | - | - | - | - | - |
| 31 | ?? | - | - | - | ???? |
| 32 | ?? | ?? | - | - | ???? |
* There is no proof of impossibility for L(3,8), only exhaustive search (I think).
Conditions for solvability:
| n | Planar P(2,n) |
End Run Planar |
Tanton's Chairs |
Colombian Variant |
|---|---|---|---|---|
| A125762 | anchor | A003111 | A336747 | |
| 1 | - | - | 1 | - |
| 2 | - | - | - | - |
| 3 | 1 | 1 | 1 | 1 |
| 4 | 0 | 1 | - | 1 |
| 5 | - | - | 3 | - |
| 6 | - | - | - | - |
| 7 | 0 | 6 | 19 | 3 |
| 8 | 4 | 24 | - | 10 |
| 9 | - | - | 225 | - |
| 10 | - | - | - | - |
| 11 | 16 | 139 | 3,441 | 76 |
| 12 | 40 | 289 | - | 140 |
| 13 | - | - | - | 79,259 |
| 14 | - | - | - | - |
| 15 | 194 | 2414 | 2,424,195 | 2,478 |
| 16 | 274 | 4455 | - | 5,454 |
| 17 | - | - | 94,471,089 | - |
| 18 | - | - | - | - |
| 19 | 2,384 | ? | 4,613,520,889 | ? |
| 20 | 4,719 | ? | - | ? |
| 21 | - | - | ? | - |
| 22 | - | - | - | - |
| 23 | 31,856 | ? | ? | ? |
| 24 | 62,124 | ? | - | ? |
| 25 | - | - | ? | - |
| 26 | - | - | - | - |
| 27 | 426,502 | ? | ? | ? |
| 28 | 817,717 | ? | - | ? |
| 29 | - | - | ? | - |
| 30 | - | - | - | - |
| 31 | 5,724,640 | ? | ? | ? |
| 32 | 10,838,471 | ? | - | ? |