A230831 - OEIS

%I #4 Oct 30 2013 20:33:54

%S 0,0,0,0,2,0,0,2,2,0,0,6,8,6,0,0,16,10,10,16,0,0,44,38,62,38,44,0,0,

%T 124,130,176,176,130,124,0,0,354,456,734,898,734,456,354,0,0,1020,

%U 1610,3034,4350,4350,3034,1610,1020,0,0,2956,5740,12962,22852,29446,22852,12962

%N T(n,k)=Number of nXk 0..3 arrays x(i,j) with each element horizontally, vertically or antidiagonally next to at least one element with value (x(i,j)+1) mod 4 and at least one element with value (x(i,j)-1) mod 4, no adjacent elements equal, and upper left element zero

%C Table starts

%C .0...0....0.....0......0.......0........0.........0..........0...........0

%C .0...2....2.....6.....16......44......124.......354.......1020........2956

%C .0...2....8....10.....38.....130......456......1610.......5740.......20556

%C .0...6...10....62....176.....734.....3034.....12962......55806......241462

%C .0..16...38...176....898....4350....22852....122740.....661598.....3593650

%C .0..44..130...734...4350...29446...201592...1388526....9649244....67351066

%C .0.124..456..3034..22852..201592..1807682..16202418..145774974..1316654208

%C .0.354.1610.12962.122740.1388526.16202418.188719562.2198502114.25739337218

%H R. H. Hardin, <a href="/A230831/b230831.txt">Table of n, a(n) for n = 1..199</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-1)

%F k=2: a(n) = 4*a(n-1) -2*a(n-2) -3*a(n-3) -a(n-4) for n>5

%F k=3: [order 12] for n>17

%F k=4: [order 46] for n>51

%e Some solutions for n=4 k=4

%e ..0..1..2..1....0..1..3..0....0..1..2..1....0..3..0..3....0..1..2..1

%e ..3..0..3..0....3..2..1..2....3..0..3..0....1..2..1..2....3..0..3..0

%e ..2..1..2..1....1..3..0..3....2..1..2..1....0..3..0..3....2..1..2..3

%e ..3..0..3..2....0..2..1..0....3..0..3..0....1..2..1..0....0..3..1..0

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Oct 30 2013