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A205753 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock having the same number of equal edges as its horizontal neighbors and a different number from its vertical neighbors, and new values 0..2 introduced in row major order.

%I A205753 #10 Jul 22 2025 19:00:38
%S A205753 14,48,74,175,284,413,677,1074,1936,2268,2709,4256,8926,12384,12574,
%T A205753 11143,16986,45985,63838,82992,69338,46709,68692,240448,383290,507035,
%U A205753 542718,383440,198483,279504,1320659,2244622,3869807,3797920,3602578
%N A205753 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock having the same number of equal edges as its horizontal neighbors and a different number from its vertical neighbors, and new values 0..2 introduced in row major order.
%C A205753 Table starts
%C A205753 ......14.......48.......175........677........2709........11143.........46709
%C A205753 ......74......284......1074.......4256.......16986........68692........279504
%C A205753 .....413.....1936......8926......45985......240448......1320659.......7401826
%C A205753 ....2268....12384.....63838.....383290.....2244622.....14131118......88143754
%C A205753 ...12574....82992....507035....3869807....28155907....233316016....1885888870
%C A205753 ...69338...542718...3797920...34977686...292986186...2917623614...26828234464
%C A205753 ..383440..3602578..29561841..341919297..3496020388..45262306396..528507252157
%C A205753 .2117054.23691830.224378004.3167656992.37842800738.599332178604.8142071823898
%H A205753 R. H. Hardin, <a href="/A205753/b205753.txt">Table of n, a(n) for n = 1..142</a>
%e A205753 Some solutions for n=4 k=3
%e A205753 ..0..1..2..1....0..0..0..0....0..1..0..2....0..0..0..1....0..1..0..2
%e A205753 ..1..1..1..1....0..0..0..0....2..0..1..0....2..2..0..0....2..2..0..1
%e A205753 ..2..0..2..0....2..1..2..1....1..0..2..2....0..1..1..2....2..0..0..1
%e A205753 ..1..2..0..1....2..1..1..1....0..0..2..0....1..1..2..2....2..1..2..1
%e A205753 ..2..2..0..0....2..0..2..0....2..1..1..1....2..0..0..1....1..2..0..2
%Y A205753 Column 1 is A205583.
%Y A205753 Row 1 is A205468.
%K A205753 nonn,tabl
%O A205753 1,1
%A A205753 _R. H. Hardin_ Jan 30 2012