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

%I #4 Feb 05 2014 06:10:09

%S 256,1280,1280,6976,10304,6976,40064,91744,91744,40064,234752,853152,

%T 1301304,853152,234752,1395200,8036672,19274172,19274172,8036672,

%U 1395200,8344576,76825568,289676104,459119016,289676104,76825568,8344576

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

%C Table starts

%C ........256.........1280............6976............40064............234752

%C .......1280........10304...........91744...........853152...........8036672

%C .......6976........91744.........1301304.........19274172.........289676104

%C ......40064.......853152........19274172........459119016.......11137777044

%C .....234752......8036672.......289676104......11137777044......437033830120

%C ....1395200.....76825568......4449131420.....278128391716....17747542016236

%C ....8344576....738844928.....68828263944....6990394415904...723439724838368

%C ...50202624...7176050400...1081186864940..179301038336988.30208726334780288

%C ..302927872..69914628864..17018044573704.4594600424879136

%C .1834229760.686426761312.271159929187820

%H R. H. Hardin, <a href="/A237241/b237241.txt">Table of n, a(n) for n = 1..84</a>

%F Empirical for column k:

%F k=1: [linear recurrence of order 11]

%F k=2: [order 22]

%F k=3: [order 67]

%e Some solutions for n=2 k=4

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Feb 05 2014