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T(n,k)=Number of (n+1)X(k+1) 0..6 arrays with every 2X2 subblock having equal diagonal elements or equal antidiagonal elements
9

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

%S 637,8281,8281,107653,254359,107653,1399489,7501753,7501753,1399489,

%T 18193357,222645367,543848893,222645367,18193357,236513641,6601376089,

%U 39572771665,39572771665,6601376089,236513641,3074677333,195759462871

%N T(n,k)=Number of (n+1)X(k+1) 0..6 arrays with every 2X2 subblock having equal diagonal elements or equal antidiagonal elements

%C Table starts

%C .........637............8281..............107653..............1399489

%C ........8281..........254359.............7501753............222645367

%C ......107653.........7501753...........543848893..........39572771665

%C .....1399489.......222645367.........39572771665........7265109130279

%C ....18193357......6601376089.......2880436707253.....1337957259758497

%C ...236513641....195759462871.....209668438383145...247090069595954263

%C ..3074677333...5804976472057...15261911634884845.45601045546133880817

%C .39970805329.172139217677623.1110925438997643073

%H R. H. Hardin, <a href="/A203887/b203887.txt">Table of n, a(n) for n = 1..60</a>

%F Empirical for columns:

%F k=1: a(n) = 49*13^n

%F k=2: a(n) = 25*a(n-1) +138*a(n-2)

%F k=3: a(n) = 79*a(n-1) -450*a(n-2) -144*a(n-3)

%F k=4: a(n) = 115*a(n-1) +17016*a(n-2) -763308*a(n-3) -1177416*a(n-4) +49714560*a(n-5) +35870688*a(n-6) -153031680*a(n-7)

%F k=5: (order 12 recurrence)

%e Some solutions for n=4 k=3

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Jan 07 2012