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%I #7 Feb 07 2014 19:26:57
%S 81,322,322,1278,1632,1278,5228,8236,8236,5228,21456,44186,53167,
%T 44186,21456,87164,238640,373804,373804,238640,87164,354008,1260486,
%U 2671962,3604930,2671962,1260486,354008,1441060,6627450,18401364,35476776
%N T(n,k)=Number of (n+1) X (k+1) 0..2 arrays with the maximum plus the upper median plus the minimum of every 2 X 2 subblock differing from its horizontal and vertical neighbors by exactly one.
%C Table starts
%C .......81.......322........1278..........5228...........21456............87164
%C ......322......1632........8236.........44186..........238640..........1260486
%C .....1278......8236.......53167........373804.........2671962.........18401364
%C .....5228.....44186......373804.......3604930........35476776........330330878
%C ....21456....238640.....2671962......35476776.......480758688.......6045609040
%C ....87164...1260486....18401364.....330330878......6045609040.....101410470742
%C ...354008...6627450...125750824....3029315052.....74740595664....1668740442760
%C ..1441060..35198148...872440876...28551327846....958854072908...28739211200900
%C ..5874828.187296514..6089994150..271444171644..12448856412422..500884807969628
%C .23898504.992298282.42113161848.2547123932136.158549359318752.8543128692901112
%H R. H. Hardin, <a href="/A237412/b237412.txt">Table of n, a(n) for n = 1..143</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 16]
%F k=2: [order 37]
%e Some solutions for n=3 k=4
%e ..0..2..1..2..0....0..2..1..0..1....0..2..0..0..2....0..2..1..1..2
%e ..1..1..1..2..0....0..0..0..1..2....1..0..2..1..2....0..0..0..1..0
%e ..0..0..2..0..1....2..1..1..2..0....1..1..1..1..0....1..0..2..1..1
%e ..1..2..0..1..0....1..1..1..1..0....2..0..0..2..2....1..0..1..1..1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Feb 07 2014
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