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%I #4 Apr 02 2014 14:06:05
%S 1,1,2,1,5,3,1,8,12,4,1,14,37,27,7,1,26,129,138,73,10,1,50,478,771,
%T 680,154,15,1,98,1908,5240,7170,2413,358,24,1,194,7868,40765,91879,
%U 44594,10017,872,35,1,386,32888,336257,1399773,1005029,333607,43956,1871,54,1
%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 one plus the sum of the elements above it or three plus the sum of the elements diagonally to its northwest, modulo 4
%C Table starts
%C ..1....1......1.........1...........1............1.............1.............1
%C ..2....5......8........14..........26...........50............98...........194
%C ..3...12.....37.......129.........478.........1908..........7868.........32888
%C ..4...27....138.......771........5240........40765........336257.......2843914
%C ..7...73....680......7170.......91879......1399773......22849697.....385366572
%C .10..154...2413.....44594.....1005029.....28061567.....865984451...28244997476
%C .15..358..10017....333607....14022582....733907809...43398047802.2752449791995
%C .24..872..43956...2715035...206345434..19388521135.2070573220929
%C .35.1871.159668..17332017..2336659626.394134037392
%C .54.4438.681760.134735700.33576330306
%H R. H. Hardin, <a href="/A240192/b240192.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 13]
%F Empirical for row n:
%F n=1: a(n) = a(n-1)
%F n=2: a(n) = 3*a(n-1) -2*a(n-2) for n>3
%F n=3: a(n) = 9*a(n-1) -27*a(n-2) +29*a(n-3) +6*a(n-4) -32*a(n-5) +16*a(n-6) for n>9
%F n=4: [order 29] for n>34
%e Some solutions for n=4 k=4
%e ..2..0..0..0....2..0..0..0....2..0..0..0....2..0..0..0....2..0..0..0
%e ..1..2..0..0....2..3..0..2....2..0..0..0....2..0..0..0....2..0..0..0
%e ..2..1..0..2....2..3..3..1....2..0..3..0....2..3..0..2....2..0..3..2
%e ..1..3..2..0....1..2..1..1....2..0..3..3....1..2..2..0....1..0..2..1
%Y Column 1 is A159288
%Y Row 2 is A164094(n-2)
%K nonn,tabl
%O 1,3
%A _R. H. Hardin_, Apr 02 2014
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