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T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with the upper median minus the lower median of every 2X2 subblock equal
7

%I #4 Feb 09 2014 05:52:41

%S 256,1692,1692,11602,23680,11602,83104,330210,330210,83104,598364,

%T 4857060,9080246,4857060,598364,4364082,70923320,266120870,266120870,

%U 70923320,4364082,31944336,1050283590,7718716424,15808900408,7718716424

%N T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with the upper median minus the lower median of every 2X2 subblock equal

%C Table starts

%C ......256........1692.........11602............83104..............598364

%C .....1692.......23680........330210..........4857060............70923320

%C ....11602......330210.......9080246........266120870..........7718716424

%C ....83104.....4857060.....266120870......15808900408........924306101684

%C ...598364....70923320....7718716424.....924306101684.....108563082111330

%C ..4364082..1050283590..228011672782...55265390979178...13080735236141448

%C .31944336.15572216080.6746760123582.3305459406659964.1575053689185059756

%H R. H. Hardin, <a href="/A237538/b237538.txt">Table of n, a(n) for n = 1..84</a>

%F Empirical for column k:

%F k=1: [linear recurrence of order 16]

%F k=2: [order 38]

%e Some solutions for n=2 k=4

%e ..0..0..0..2..0....0..0..2..3..2....0..0..2..3..1....0..0..2..2..0

%e ..1..0..2..2..2....1..2..1..0..1....0..2..3..3..3....0..2..2..2..3

%e ..1..2..2..2..0....1..2..1..0..3....0..0..2..3..2....2..3..1..2..0

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Feb 09 2014