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T(n,k)=Number of (n+1)X(k+1) 0..7 arrays with every 2X2 subblock having equal diagonal elements or equal antidiagonal elements
4

%I #5 Mar 31 2012 12:36:58

%S 960,14400,14400,216000,539456,216000,3240000,19071424,19071424,

%T 3240000,48600000,681461824,1754118528,681461824,48600000,729000000,

%U 24301391808,161916229056,161916229056,24301391808,729000000,10935000000

%N T(n,k)=Number of (n+1)X(k+1) 0..7 arrays with every 2X2 subblock having equal diagonal elements or equal antidiagonal elements

%C Table starts

%C ..........960..........14400...........216000..........3240000.........48600000

%C ........14400.........539456.........19071424........681461824......24301391808

%C .......216000.......19071424.......1754118528.....161916229056...14950234495680

%C ......3240000......681461824.....161916229056...39986164706496.9889622728751424

%C .....48600000....24301391808...14950234495680.9889622728751424

%C ....729000000...866928276544.1380434809882752

%C ..10935000000.30924651270080

%C .164025000000

%H R. H. Hardin, <a href="/A203732/b203732.txt">Table of n, a(n) for n = 1..40</a>

%F Empirical for column k:

%F k=1: a(n) = 64*15^n

%F k=2: a(n) = 29*a(n-1) +238*a(n-2)

%F k=3: a(n) = 99*a(n-1) -609*a(n-2) -588*a(n-3)

%F k=4: a(n) = 141*a(n-1) +34391*a(n-2) -1914087*a(n-3) -5360404*a(n-4) +185626112*a(n-5) +226020536*a(n-6) -801895584*a(n-7)

%e Some solutions for n=4 k=3

%e ..4..0..2..1....2..3..7..4....0..4..1..2....3..2..0..1....4..7..7..3

%e ..1..4..0..2....4..2..3..7....0..0..4..1....0..3..2..0....2..4..7..7

%e ..0..1..4..0....6..4..2..3....5..0..0..4....7..0..3..2....0..2..4..7

%e ..2..0..1..4....6..6..4..2....1..5..0..0....1..7..0..3....3..0..2..4

%e ..5..2..0..1....1..6..6..4....5..0..3..0....5..1..7..0....7..3..0..2

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Jan 05 2012