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A203835 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock having equal diagonal elements or equal antidiagonal elements.

%I A203835 #7 Jul 22 2025 17:33:04
%S A203835 45,225,225,1125,1971,1125,5625,17289,17289,5625,28125,151659,270333,
%T A203835 151659,28125,140625,1330353,4238721,4238721,1330353,140625,703125,
%U A203835 11669859,66490965,119606211,66490965,11669859,703125,3515625,102368025
%N A203835 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock having equal diagonal elements or equal antidiagonal elements.
%C A203835 Table starts
%C A203835 ......45.......225.........1125...........5625.............28125
%C A203835 .....225......1971........17289.........151659...........1330353
%C A203835 ....1125.....17289.......270333........4238721..........66490965
%C A203835 ....5625....151659......4238721......119606211........3383285769
%C A203835 ...28125...1330353.....66490965.....3383285769......173185290765
%C A203835 ..140625..11669859...1043088057....95763046491.....8882824128417
%C A203835 ..703125.102368025..16363800045..2710984443345...455911325162757
%C A203835 .3515625.897972507.256713156657.76749227497395.23404859123410809
%H A203835 R. H. Hardin, <a href="/A203835/b203835.txt">Table of n, a(n) for n = 1..144</a>
%F A203835 Empirical for column k:
%F A203835 k=1: a(n) = 9*5^n
%F A203835 k=2: a(n) = 9*a(n-1) -2*a(n-2)
%F A203835 k=3: a(n) = 19*a(n-1) -54*a(n-2) +32*a(n-3)
%F A203835 k=4: a(n) = 31*a(n-1) -24*a(n-2) -1612*a(n-3) +3816*a(n-4) +1152*a(n-5) -2784*a(n-6) +256*a(n-7)
%F A203835 k=5: (order 12 recurrence)
%F A203835 k=6: (order 28 recurrence)
%F A203835 k=7: (order 54 recurrence)
%e A203835 Some solutions for n=4 k=3
%e A203835 ..0..2..0..1....2..1..0..0....0..1..2..0....0..0..2..0....2..1..0..2
%e A203835 ..2..0..1..0....1..1..1..0....1..2..2..2....0..2..2..2....2..2..1..0
%e A203835 ..0..2..0..1....2..1..2..1....0..1..2..2....1..0..2..2....1..2..2..1
%e A203835 ..2..0..0..0....2..2..2..2....0..0..1..2....2..1..0..2....0..1..2..2
%e A203835 ..2..2..0..1....1..2..1..2....2..0..0..1....1..2..1..0....2..0..1..2
%Y A203835 Column 1 is A189274(n+2)
%K A203835 nonn,tabl
%O A203835 1,1
%A A203835 _R. H. Hardin_ Jan 06 2012