A231285 - OEIS

%I #4 Nov 06 2013 18:31:49

%S 0,0,0,0,0,0,0,2,0,0,0,6,8,0,0,0,26,76,66,0,0,0,118,834,1170,400,0,0,

%T 0,522,9488,34786,18208,2722,0,0,0,2310,105962,1083188,1400418,278758,

%U 17688,0,0,0,10234,1179364,31513702,113949472,56442770,4294812,117026,0

%N T(n,k)=Number of nXk 0..3 arrays x(i,j) with each element horizontally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, and upper left element zero

%C Table starts

%C .0.0......0........0...........0...............0..................0

%C .0.0......2........6..........26.............118................522

%C .0.0......8.......76.........834............9488.............105962

%C .0.0.....66.....1170.......34786.........1083188...........31513702

%C .0.0....400....18208.....1400418.......113949472.........8501873308

%C .0.0...2722...278758....56442770.....12128733980......2336016267460

%C .0.0..17688..4294812..2276141330...1290580702666....640923626812310

%C .0.0.117026.66052162.91775666754.137311555002556.175842069555560942

%H R. H. Hardin, <a href="/A231285/b231285.txt">Table of n, a(n) for n = 1..143</a>

%F Empirical for column k:

%F k=3: a(n) = 4*a(n-1) +17*a(n-2)

%F k=4: a(n) = 9*a(n-1) +86*a(n-2) +190*a(n-3) -29*a(n-4) +a(n-5)

%F k=5: [order 10] for n>11

%F k=6: [order 30] for n>31

%F k=7: [order 55] for n>57

%F Empirical for row n:

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

%F n=3: [order 19] for n>21

%e Some solutions for n=3 k=4

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

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

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

%Y Row 2 is A230245(n-1)

%K nonn,tabl

%O 1,8

%A _R. H. Hardin_, Nov 06 2013