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%I #4 Dec 16 2013 18:23:15
%S 216,1040,1040,4640,4824,4640,22592,22472,22472,22592,104576,129728,
%T 106304,129728,104576,511232,699984,716800,716800,699984,511232,
%U 2416128,4332592,4319616,5783176,4319616,4332592,2416128,11843584,24793848
%N T(n,k)=Number of (n+1)X(k+1) 0..7 arrays with every 2X2 subblock having the sum of the squares of all six edge and diagonal differences equal to 59 (59 maximizes T(1,1))
%C Table starts
%C .......216.......1040.........4640........22592.......104576.......511232
%C ......1040.......4824........22472.......129728.......699984......4332592
%C ......4640......22472.......106304.......716800......4319616.....34000600
%C .....22592.....129728.......716800......5783176.....41245344....408524804
%C ....104576.....699984......4319616.....41245344....337818824...4191443728
%C ....511232....4332592.....34000600....408524804...4191443728..63517858688
%C ...2416128...24793848....226756256...3305571808..40029477624.748312618740
%C ..11843584..156146264...1873475872..36165120612.580040050696
%C ..56662016..917982376..13046763360.311162540132
%C .278233088.5792726088.108927798728
%H R. H. Hardin, <a href="/A233859/b233859.txt">Table of n, a(n) for n = 1..84</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 14]
%F k=2: [order 68]
%e Some solutions for n=3 k=4
%e ..0..4..1..4..5....4..1..2..1..4....4..5..2..5..2....4..6..1..6..6
%e ..5..2..6..2..0....6..2..6..2..6....4..0..4..0..4....1..2..2..2..7
%e ..0..4..1..4..5....6..7..4..1..2....5..2..5..4..5....2..6..1..6..4
%e ..5..2..6..2..0....2..6..2..6..2....0..4..0..4..0....1..2..2..2..1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 16 2013