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A183827 T(n,k)=1/256 the number of (n+1)X(k+1) 0..3 arrays with no 2X2 subblock being a reflection across the shared element pair of any horizontal or vertical neighbor.

%I A183827 #7 Jul 22 2025 09:13:23
%S A183827 1,15,15,225,813,225,3375,43947,43947,3375,50625,2377341,8538066,
%T A183827 2377341,50625,759375,128578815,1661285961,1661285961,128578815,
%U A183827 759375,11390625,6954559893,323115202755,1163575148283,323115202755,6954559893,11390625
%N A183827 T(n,k)=1/256 the number of (n+1)X(k+1) 0..3 arrays with no 2X2 subblock being a reflection across the shared element pair of any horizontal or vertical neighbor.
%C A183827 Table starts
%C A183827 ...........1...............15.................225..................3375
%C A183827 ..........15..............813...............43947...............2377341
%C A183827 .........225............43947.............8538066............1661285961
%C A183827 ........3375..........2377341..........1661285961.........1163575148283
%C A183827 .......50625........128578815........323115202755.......814479338538099
%C A183827 ......759375.......6954559893......62851591581012....570213177028325955
%C A183827 ....11390625.....376152548283...12225396762980829.399185865558804067443
%C A183827 ...170859375...20345104031589.2378005715920214025
%C A183827 ..2562890625.1100412240703119
%C A183827 .38443359375
%H A183827 R. H. Hardin, <a href="/A183827/b183827.txt">Table of n, a(n) for n = 1..60</a>
%e A183827 Some solutions with upper left block zero for 4X3
%e A183827 ..0..0..0....0..0..3....0..0..2....0..0..2....0..0..0....0..0..1....0..0..1
%e A183827 ..0..0..1....0..0..3....0..0..2....0..0..1....0..0..2....0..0..3....0..0..1
%e A183827 ..1..0..3....1..2..0....0..3..2....2..1..1....2..2..0....2..3..0....1..0..3
%e A183827 ..3..3..0....2..2..2....0..2..3....3..1..1....1..3..3....2..2..1....1..0..0
%Y A183827 Column 1 is A001024(n-1)
%K A183827 nonn,tabl
%O A183827 1,2
%A A183827 _R. H. Hardin_ Jan 07 2011