[seqfan] Quick puzzle encounterd

[Ron Hardin]

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)