%I #4 Apr 02 2014 09:20:41

%S 2,3,3,4,5,4,7,8,11,7,10,19,20,25,10,15,36,107,67,62,15,24,57,186,676,

%T 254,144,24,35,120,450,1328,3993,825,329,35,54,218,1641,5701,11742,

%U 22412,2667,775,54,83,377,2788,24419,88214,108201,131005,8652,1781,83,124,758

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

%C Table starts

%C ..2....3.....4........7.........10..........15..........24.........35

%C ..3....5.....8.......19.........36..........57.........120........218

%C ..4...11....20......107........186.........450........1641.......2788

%C ..7...25....67......676.......1328........5701.......24419......52676

%C .10...62...254.....3993......11742.......88214......536744....1652584

%C .15..144...825....22412.....108201.....1608415....12812998...70360014

%C .24..329..2667...131005....1056699....30542203...417799464.3795213209

%C .35..775..8652...731518...10526838...584983851.14482686630

%C .54.1781.27929..4144347..107361960.11643589675

%C .83.4150.91436.23263202.1116331018

%H R. H. Hardin, <a href="/A240153/b240153.txt">Table of n, a(n) for n = 1..112</a>

%F Empirical for column k:

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

%F k=2: [order 34] for n>36

%F Empirical for row n:

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

%F n=2: [order 17] for n>19

%e Some solutions for n=4 k=4

%e ..2..2..3..2....2..2..3..3....2..2..3..3....2..2..3..3....2..2..3..3

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

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

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

%Y Row and column 1 are A159288(n+1)

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Apr 02 2014