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%I #6 May 28 2021 14:52:18
%S 256,1608,1608,10664,15800,10664,72584,165780,165780,72584,499560,
%T 1792226,2842692,1792226,499560,3342416,18918620,51036456,51036456,
%U 18918620,3342416,22488016,202875630,961463420,1809464182,961463420
%N T(n,k) = Number of (n+1) X (k+1) 0..3 arrays with the maximum plus the upper median of every 2 X 2 subblock differing from its horizontal and vertical neighbors by exactly one.
%C Table starts
%C .......256........1608.........10664............72584..............499560
%C ......1608.......15800........165780..........1792226............18918620
%C .....10664......165780.......2842692.........51036456...........961463420
%C .....72584.....1792226......51036456.......1809464182.........63323756608
%C ....499560....18918620.....961463420......63323756608.......4251191656884
%C ...3342416...202875630...18066348584....2281444628340.....277864575306608
%C ..22488016..2177434900..345494546192...79094196555400...18866641119536914
%C .152285824.23302931502.6395305423256.2844505175089988.1284534193930221572
%H R. H. Hardin, <a href="/A238155/b238155.txt">Table of n, a(n) for n = 1..112</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 20] for n > 21.
%F k=2: [order 56] for n > 58.
%e Some solutions for n=2, k=4
%e ..1..0..2..1..3....1..0..2..1..3....0..0..3..1..2....1..0..1..0..2
%e ..3..2..1..1..0....1..3..2..1..2....2..2..2..3..0....2..1..0..2..1
%e ..2..3..2..2..3....2..0..3..1..2....3..1..2..0..3....2..0..2..0..0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Feb 18 2014
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