A231246 - OEIS

%I #4 Nov 06 2013 05:41:22

%S 0,0,0,0,2,0,0,14,6,0,0,44,78,20,0,0,146,464,552,68,0,0,572,3090,5992,

%T 3820,230,0,0,2258,22460,76264,76136,26658,778,0,0,8660,162766,

%U 1081934,1872136,968824,185074,2632,0,0,33026,1169472,15270416,52280836,46019438

%N T(n,k)=Number of nXk 0..3 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to 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

%C .0....2......14........44.........146...........572.............2258

%C .0....6......78.......464........3090.........22460...........162766

%C .0...20.....552......5992.......76264.......1081934.........15270416

%C .0...68....3820.....76136.....1872136......52280836.......1450042214

%C .0..230...26658....968824....46019438....2532190370.....138246711032

%C .0..778..185074..12322784..1130422470..122516675112...13176773912306

%C .0.2632.1287036.156753000.27772974680.5929632659798.1256579264497704

%H R. H. Hardin, <a href="/A231246/b231246.txt">Table of n, a(n) for n = 1..161</a>

%F Empirical for column k:

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

%F k=3: a(n) = 4*a(n-1) +16*a(n-2) +26*a(n-3) +37*a(n-4) +6*a(n-5)

%F k=4: a(n) = 10*a(n-1) +30*a(n-2) +53*a(n-3) +71*a(n-4) -a(n-5) +6*a(n-6) -8*a(n-7)

%F k=5: [order 19]

%F k=6: [order 74]

%F Empirical for row n:

%F n=2: a(n) = 4*a(n-1) -3*a(n-2) +8*a(n-3) +4*a(n-4) for n>5

%F n=3: [order 7] for n>8

%F n=4: [order 22] for n>23

%F n=5: [order 62] for n>63

%e Some solutions for n=2 k=4

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

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

%Y Column 2 is A231057

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Nov 06 2013