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A186218 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock determinant equal to some horizontal or vertical neighbor 2X2 subblock determinant.

%I A186218 #7 Jul 22 2025 10:20:04
%S A186218 0,175,175,609,1969,609,3593,18873,18873,3593,15055,197619,308593,
%T A186218 197619,15055,76263,2008031,6275745,6275745,2008031,76263,353985,
%U A186218 20738153,116461359,255375977,116461359,20738153,353985,1729733,213108423
%N A186218 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock determinant equal to some horizontal or vertical neighbor 2X2 subblock determinant.
%C A186218 Table starts
%C A186218 ........0.........175..........609...........3593..........15055..........76263
%C A186218 ......175........1969........18873.........197619........2008031.......20738153
%C A186218 ......609.......18873.......308593........6275745......116461359.....2259545215
%C A186218 .....3593......197619......6275745......255375977.....9406230423...363322785761
%C A186218 ....15055.....2008031....116461359.....9406230423...660028898887.49524283508081
%C A186218 ....76263....20738153...2259545215...363322785761.49524283508081
%C A186218 ...353985...213108423..43035959317.13767728347159
%C A186218 ..1729733..2194753479.826432933951
%C A186218 ..8225815.22587046821
%C A186218 .39664199
%H A186218 R. H. Hardin, <a href="/A186218/b186218.txt">Table of n, a(n) for n = 1..60</a>
%e A186218 Some solutions for 4X3
%e A186218 ..1..0..0....0..0..1....2..2..2....2..0..2....2..2..2....1..2..0....1..2..1
%e A186218 ..1..0..1....2..0..2....2..1..0....0..0..1....1..1..1....0..0..0....0..0..0
%e A186218 ..2..0..1....1..0..0....0..0..0....0..0..2....1..1..1....2..2..2....0..1..2
%e A186218 ..0..0..1....0..0..0....2..0..1....1..0..0....2..1..0....0..0..0....0..1..2
%K A186218 nonn,tabl
%O A186218 1,2
%A A186218 _R. H. Hardin_ Feb 15 2011