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A237332 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with the maximum plus the upper median plus the lower median minus the minimum of every 2X2 subblock differing from its horizontal and vertical neighbors by exactly one.

%I A237332 #6 Jul 23 2025 10:05:49
%S A237332 81,320,320,1264,1660,1264,5120,8588,8588,5120,20692,45996,58296,
%T A237332 45996,20692,82800,242644,414268,414268,242644,82800,332192,1279474,
%U A237332 2870224,3988852,2870224,1279474,332192,1346016,6740992,19874388,36921568
%N A237332 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with the maximum plus the upper median plus the lower median minus the minimum of every 2X2 subblock differing from its horizontal and vertical neighbors by exactly one.
%C A237332 Table starts
%C A237332 .......81........320........1264..........5120...........20692...........82800
%C A237332 ......320.......1660........8588.........45996..........242644.........1279474
%C A237332 .....1264.......8588.......58296........414268.........2870224........19874388
%C A237332 .....5120......45996......414268.......3988852........36921568.......342809906
%C A237332 ....20692.....242644.....2870224......36921568.......449909120......5467718444
%C A237332 ....82800....1279474....19874388.....342809906......5467718444.....88161950500
%C A237332 ...332192....6740992...137663582....3194951224.....67160833084...1426506722524
%C A237332 ..1346016...36117846...978134492...31126440590....873971263352..24924114752042
%C A237332 ..5439936..190631336..6780688008..290583883424..10725570823166.399514227564720
%C A237332 .21769152.1005363146.46959680920.2718308070358.130884937973764
%H A237332 R. H. Hardin, <a href="/A237332/b237332.txt">Table of n, a(n) for n = 1..112</a>
%F A237332 Empirical for column k:
%F A237332 k=1: a(n) = 288*a(n-4) -6720*a(n-8) +33536*a(n-12) for n>15
%F A237332 k=2: [order 32] for n>34
%e A237332 Some solutions for n=3 k=4
%e A237332 ..0..1..0..2..2....0..2..1..0..2....0..0..1..2..2....0..1..0..1..1
%e A237332 ..0..1..1..1..2....2..1..2..0..2....2..1..2..2..2....1..0..2..1..0
%e A237332 ..0..2..2..1..0....1..0..0..2..1....1..0..2..2..1....0..0..0..0..1
%e A237332 ..2..0..1..2..2....0..2..2..1..2....2..2..2..1..0....1..1..2..0..0
%K A237332 nonn,tabl
%O A237332 1,1
%A A237332 _R. H. Hardin_, Feb 06 2014