# [seqfan] Knight's tour A186441

Ron Hardin rhhardin at att.net
Wed Feb 23 01:05:50 CET 2011

```Doing a T(n,k) version of http://oeis.org/A186441 for n steps on a (k+2)X(k+2)
board, it doesn't look like it's agreeing (column 6)

T(n,k)=Number of n-step knight's tours on a (k+2)X(k+2) board summed over all
starting positions
Table starts
..9...16.....25......36......49.....64.....81...100...121..144..169..196.225
.16...48.....96.....160.....240....336....448...576...720..880.1056.1248....
.16..104....328.....664....1112...1672...2344..3128..4024.5032.6152.........
.16..208....976....2576....5056...8320..12368.17200.22816...................
.16..400...2800....9328...21480..39616..63440.92656.........................
.16..800...8352...34448...91328.186544.322528...............................
.16.1280..21664..118480..372384.847520......................................
.16.2208..57392..405040.1508784.............................................
..0.3184.135184.1290112.....................................................
..0.4640.317296.............................................................
..0.5184....................................................................
..0.........................................................................

more terms being computed (not very efficiently timewise, but rather
script-change minimizing).

I assume knight's tour means no repeated positions.

Also obviously then each column is finite, going to 0 after the board is filled.

---rhhardin at mindspring.com
rhhardin at att.net (either)

```