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%I #4 Apr 03 2014 09:43:27
%S 2,4,3,10,7,4,24,35,14,7,56,157,118,36,10,132,713,919,582,72,15,312,
%T 3263,7562,8265,2000,170,24,736,14895,64721,126286,49921,8353,411,35,
%U 1736,68101,563496,2059061,1363144,382690,37422,879,54,4096,311509,4956889
%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 one plus the sum of the elements diagonally to its northwest, modulo 4
%C Table starts
%C ..2....4......10.........24..........56..........132...........312
%C ..3....7......35........157.........713.........3263.........14895
%C ..4...14.....118........919........7562........64721........563496
%C ..7...36.....582.......8265......126286......2059061......34514871
%C .10...72....2000......49921.....1363144.....40760821....1277623744
%C .15..170....8353.....382690....19210586...1063706501...63085436203
%C .24..411...37422....3076452...278945445..27923918285.3004792552569
%C .35..879..135463...19781372..3200032085.576407548906
%C .54.2106..580528..154994425.46095401280
%C .83.4874.2403439.1144262410
%H R. H. Hardin, <a href="/A240271/b240271.txt">Table of n, a(n) for n = 1..97</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) = 2*a(n-1) +2*a(n-3)
%F n=2: [order 26] for n>28
%e Some solutions for n=4 k=4
%e ..2..3..0..3....3..2..2..2....3..0..0..2....3..0..2..0....3..2..2..2
%e ..2..1..2..3....3..1..2..1....2..3..2..0....2..3..0..2....2..1..2..0
%e ..2..0..1..0....2..1..2..2....3..1..2..0....3..1..1..0....3..2..0..2
%e ..2..0..1..0....2..0..0..1....3..2..2..0....3..2..2..1....2..3..2..2
%Y Column 1 is A159288(n+1)
%Y Row 1 is A052912
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Apr 03 2014
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