[seqfan] Quick puzzle encounterd

Ron Hardin rhhardin at att.net
Tue Nov 30 23:19:51 CET 2010

```I'm just now starting on a survey of the afternoon's project

T(n,k)=Number of nXk 0..3 arrays with no element equal to the sum mod 4 of its
neighbors

which survey traditionally begins with a fast table
Table starts
....3......12........27.........81........252..........729........2187.....6588.19683

...12......81.......776.......6561......59292.......531441.....4786704.43046721......

...27.....776.....19683.....531441...14369472....387420489.10460353203...............

...81....6561....531441...43146816.3486784401.282429536481...........................

..252...59292..14369472.3486784401...................................................

..729..531441.387420489..............................................................

.2187.4786704........................................................................

.6588................................................................................

to check what columns already exist in OEIS and so forth, and also whether to
divide out some constant from all the numbers.

Which leads to the strange puzzle that the only number (so far) that's not
divisible by 3 is 776, for a 3X2 (or 2X3) array.

Any idea why that size is special?  Therein is the question.

I have no strong feelings that any of the numbers ought to be divisible by
three, but some strong feelings that there ought not to be only one exception.

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

```