%I #4 Apr 03 2014 16:06:08

%S 2,4,2,8,6,4,16,26,24,4,32,90,206,56,8,64,340,1322,974,230,8,128,1194,

%T 9970,12164,8064,552,16,256,4424,63892,180886,200864,38252,2270,16,

%U 512,15766,459420,2228098,5967512,1867678,316962,5456,32,1024,57754,2983714

%N T(n,k)=Number of nXk 0..3 arrays with no element equal to zero plus the sum of elements to its left or two plus the sum of the elements above it or two plus the sum of the elements diagonally to its northwest, modulo 4

%C Table starts

%C ..2.....4........8..........16............32.............64............128

%C ..2.....6.......26..........90...........340...........1194...........4424

%C ..4....24......206........1322..........9970..........63892.........459420

%C ..4....56......974.......12164........180886........2228098.......31650312

%C ..8...230.....8064......200864.......5967512......144185218.....4068505132

%C ..8...552....38252.....1867678.....109846410.....5231971212...293426742772

%C .16..2270...316962....31042576....3655313420...346662397488.38864331960018

%C .16..5456..1502948...289075166...67561324734.12734002906536

%C .32.22416.12468758..4812019390.2255342381120

%C .32.53864.59122266.44835430372

%H R. H. Hardin, <a href="/A240295/b240295.txt">Table of n, a(n) for n = 1..97</a>

%F Empirical for column k:

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

%F k=2: a(n) = 12*a(n-2) -24*a(n-4) +31*a(n-6) -16*a(n-8) for n>9

%F k=3: [order 48] for n>50

%F Empirical for row n:

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

%F n=2: [order 12]

%F n=3: [order 80] for n>81

%e Some solutions for n=4 k=4

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

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

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

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

%Y Column 1 is A016116(n+1)

%Y Row 1 is A000079

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Apr 03 2014