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%I #6 Nov 12 2022 19:40:04
%S 96,444,444,1992,2624,1992,9100,16004,16004,9100,41256,103152,136960,
%T 103152,41256,187780,662008,1291820,1291820,662008,187780,853104,
%U 4295540,12203480,18407992,12203480,4295540,853104,3879380,27795204,117736088
%N T(n,k) = Number of (n+1) X (k+1) 0..4 arrays with every 2 X 2 subblock having the sum of the squares of the edge differences equal to 14 (14 maximizes T(1,1)).
%C Table starts
%C .......96........444..........1992............9100.............41256
%C ......444.......2624.........16004..........103152............662008
%C .....1992......16004........136960.........1291820..........12203480
%C .....9100.....103152.......1291820........18407992.........265416076
%C ....41256.....662008......12203480.......265416076........5886720368
%C ...187780....4295540.....117736088......3941219232......135854016892
%C ...853104...27795204....1132387344.....58415215048.....3129633625144
%C ..3879380..180350552...10952782784....873119150720....72969887485252
%C .17632896.1168954616..105752474712..13022224846292..1696131249929176
%C .80165004.7582779720.1022915229556.194807536465768.39606967139987452
%H R. H. Hardin, <a href="/A233717/b233717.txt">Table of n, a(n) for n = 1..143</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 8];
%F k=2: [order 27];
%F k=3: [order 75].
%e Some solutions for n=3, k=4
%e ..0..0..2..0..2....0..0..0..0..0....0..3..3..3..0....0..3..3..3..0
%e ..1..3..3..3..3....1..3..2..3..2....1..1..4..1..1....0..1..4..1..1
%e ..1..0..2..0..1....0..0..0..3..0....0..3..4..3..4....3..3..3..3..0
%e ..1..3..3..3..1....1..3..1..3..1....0..1..4..1..1....0..1..0..2..0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 15 2013
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