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A187699 T(n,k)=Number of (n+1)X(n+1) 0..k arrays with each 2X2 subblock determinant nonzero and the array of 2X2 subblock determinants symmetric under horizontal and vertical reflection.

%I A187699 #6 Jul 22 2025 10:53:00
%S A187699 6,50,0,192,8,104,512,74,7954,0,1126,280,87258,1548,9350,2146,784,
%T A187699 692410,22738,15128848,0,3760,1970,2363474,320674,1089964504,454640,
%U A187699 4280018,6112,3580,10839282,1147854
%N A187699 T(n,k)=Number of (n+1)X(n+1) 0..k arrays with each 2X2 subblock determinant nonzero and the array of 2X2 subblock determinants symmetric under horizontal and vertical reflection.
%C A187699 Table starts
%C A187699 .......6.......50........192....512....1126.....2146.3760.6112
%C A187699 .......0........8.........74....280.....784.....1970.3580
%C A187699 .....104.....7954......87258.692410.2363474.10839282
%C A187699 .......0.....1548......22738.320674.1147854
%C A187699 ....9350.15128848.1089964504
%C A187699 .......0...454640
%C A187699 .4280018
%e A187699 Some k=3 solutions for 5X5
%e A187699 ..1..0..1..1..2....3..2..3..1..0....2..1..3..2..3....1..2..3..1..2
%e A187699 ..0..1..1..0..1....3..3..3..0..3....1..2..3..1..3....2..1..3..2..1
%e A187699 ..1..1..2..1..2....2..1..2..1..1....2..1..3..2..3....1..2..3..1..2
%e A187699 ..1..0..1..1..1....3..0..3..3..0....3..0..3..3..3....0..3..3..0..3
%e A187699 ..3..1..2..1..2....3..1..3..2..1....3..1..2..1..2....1..2..3..1..2
%Y A187699 Row 1 is A062801
%Y A187699 Row 2 is A187529
%K A187699 nonn,tabl
%O A187699 1,1
%A A187699 _R. H. Hardin_ Mar 12 2011