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%I #5 Dec 18 2014 09:10:33
%S 478,1048,850,2532,3880,2142,5608,15480,15480,4644,14824,43848,88146,
%T 43848,13104,38780,213120,331884,331884,213120,33852,89048,881848,
%U 2576592,1179792,2576592,881848,73800,237360,2568432,15204660,11206944
%N T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock row and diagonal sum equal to 1 3 4 6 or 7 and every 3X3 column and antidiagonal sum not equal to 1 3 4 6 or 7
%C Table starts
%C .....478......1048........2532........5608..........14824...........38780
%C .....850......3880.......15480.......43848.........213120..........881848
%C ....2142.....15480.......88146......331884........2576592........15204660
%C ....4644.....43848......331884.....1179792.......11206944........84935088
%C ...13104....213120.....2576592....11206944......187695936......2316305760
%C ...33852....881848....15204660....84935088.....2316305760.....38252054800
%C ...73800...2568432....65274264...301990464....10519316352....267361717440
%C ..208992..12681664...519308064..2868905088...177838495488...7328287959424
%C ..540792..53297808..3103786152.21743273664..2214324086400.113662014539328
%C .1179792.157483872.14646511152.77309413632.10320806426112.959873651073792
%H R. H. Hardin, <a href="/A252544/b252544.txt">Table of n, a(n) for n = 1..612</a>
%F Empirical: T(n,k) is symmetric for n and k both greater than 1.
%F Empirical for column k:
%F k=1: a(n) = 18*a(n-3) -32*a(n-6) for n>8
%F k=2: a(n) = 118*a(n-3) -4264*a(n-6) +55168*a(n-9) -225280*a(n-12) +262144*a(n-15) for n>16
%F k=3: a(n) = 454*a(n-3) -60040*a(n-6) +2444800*a(n-9) -13041664*a(n-12) +16777216*a(n-15) for n>16
%F k=4: a(n) = 260*a(n-3) -1024*a(n-6) for n>7
%F k=5: a(n) = 1804*a(n-3) -939040*a(n-6) +145285120*a(n-9) -1639972864*a(n-12) +4294967296*a(n-15) for n>16
%F k=6: a(n) = 7180*a(n-3) -14766112*a(n-6) +8766324736*a(n-9) -103548977152*a(n-12) +274877906944*a(n-15) for n>16
%F k=7: a(n) = 4104*a(n-3) -32768*a(n-6) for n>7
%F Empirical for row n:
%F n=1: a(n) = 34*a(n-3) +2*a(n-5) -320*a(n-6) -36*a(n-8) +512*a(n-9) +64*a(n-11) for n>15
%F n=2: a(n) = 118*a(n-3) -4264*a(n-6) +55168*a(n-9) -225280*a(n-12) +262144*a(n-15) for n>16
%F n=3: a(n) = 454*a(n-3) -60040*a(n-6) +2444800*a(n-9) -13041664*a(n-12) +16777216*a(n-15)
%F n=4: a(n) = 260*a(n-3) -1024*a(n-6)
%F n=5: a(n) = 1804*a(n-3) -939040*a(n-6) +145285120*a(n-9) -1639972864*a(n-12) +4294967296*a(n-15)
%F n=6: a(n) = 7180*a(n-3) -14766112*a(n-6) +8766324736*a(n-9) -103548977152*a(n-12) +274877906944*a(n-15)
%F n=7: a(n) = 4104*a(n-3) -32768*a(n-6)
%e Some solutions for n=3 k=4
%e ..1..0..3..1..0..3....3..3..1..0..3..1....2..0..2..2..3..2....0..1..0..0..1..0
%e ..0..1..0..3..1..3....1..0..0..1..3..3....0..0..1..3..3..1....0..0..1..3..3..1
%e ..1..1..2..1..1..2....1..2..1..1..2..1....0..2..2..0..2..2....2..1..1..2..1..1
%e ..1..3..3..1..3..0....0..0..1..0..3..1....2..0..2..2..0..2....3..1..0..3..1..0
%e ..0..1..3..0..1..0....1..3..3..1..0..0....3..3..1..0..0..1....3..3..1..3..0..1
%Y Row 4 and column 4 are A252239 for n>1
%Y Row 7 and column 7 are A252242 for n>1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 18 2014
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