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%I #4 Dec 14 2013 08:16:38
%S 24,90,90,324,534,324,1188,3004,3004,1188,4320,17424,26192,17424,4320,
%T 15768,99380,238570,238570,99380,15768,57456,572192,2118568,3455622,
%U 2118568,572192,57456,209520,3277236,19123682,48384788,48384788,19123682
%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock having the sum of the squares of the edge differences equal to 2 (2 maximizes T(1,1))
%C Table starts
%C ......24........90..........324...........1188.............4320
%C ......90.......534.........3004..........17424............99380
%C .....324......3004........26192.........238570..........2118568
%C ....1188.....17424.......238570........3455622.........48384788
%C ....4320.....99380......2118568.......48384788.......1060656512
%C ...15768....572192.....19123682......694104494......24003655980
%C ...57456...3277236....170872144.....9797170648.....531400908604
%C ..209520..18825580...1536664586...139850230232...11957878063196
%C ..763776.107963840..13763062452..1981047775126..265950544067684
%C .2784672.619734876.123586823454.28211321138046.5965795563741028
%H R. H. Hardin, <a href="/A233644/b233644.txt">Table of n, a(n) for n = 1..312</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1) +6*a(n-2)
%F k=2: a(n) = 6*a(n-1) +9*a(n-2) -67*a(n-3) +26*a(n-4) +81*a(n-5) -48*a(n-6) +2*a(n-7)
%F k=3: [order 13]
%F k=4: [order 31]
%F k=5: [order 66]
%e Some solutions for n=3 k=4
%e ..0..0..0..1..1....2..1..2..2..2....1..0..1..0..0....1..1..1..1..1
%e ..0..1..1..1..0....1..1..1..1..1....1..0..1..0..1....0..0..1..2..1
%e ..1..1..0..1..0....0..0..0..0..0....0..0..1..1..1....1..1..1..1..1
%e ..0..1..0..1..0....0..1..1..0..1....1..0..0..1..2....1..2..2..2..1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 14 2013
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