%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