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A186553 T(n,k)=1/8192 the number of (n+2)X(k+2) 0..3 arrays with each 3X3 subblock trace equal to some horizontal or vertical neighbor 3X3 subblock trace.

%I A186553 #7 Jul 22 2025 10:24:33
%S A186553 0,290,290,2972,19016,2972,168200,1279862,1279862,168200,3090668,
%T A186553 88662978,177942264,88662978,3090668,111188198,6215002266,31976088817,
%U A186553 31976088817,6215002266,111188198,2585394080,435599518160,5253540132125
%N A186553 T(n,k)=1/8192 the number of (n+2)X(k+2) 0..3 arrays with each 3X3 subblock trace equal to some horizontal or vertical neighbor 3X3 subblock trace.
%C A186553 Table starts
%C A186553 ...........0..............290.................2972................168200
%C A186553 .........290............19016..............1279862..............88662978
%C A186553 ........2972..........1279862............177942264...........31976088817
%C A186553 ......168200.........88662978..........31976088817........13544245035035
%C A186553 .....3090668.......6215002266........5253540132125......5541254050323697
%C A186553 ...111188198.....435599518160......891778365437358...2292090739550640497
%C A186553 ..2585394080...30577245619492...149628929202973235.945658119457845662613
%C A186553 .78931270418.2145961447892386.25212444270769802733
%H A186553 R. H. Hardin, <a href="/A186553/b186553.txt">Table of n, a(n) for n = 1..59</a>
%e A186553 Some solutions for 5X4
%e A186553 ..0..2..0..0....0..2..0..0....2..2..0..0....0..2..0..0....0..2..0..0
%e A186553 ..0..2..0..0....2..0..0..0....0..0..0..0....2..2..0..0....0..0..0..0
%e A186553 ..3..2..0..0....1..0..2..0....1..0..0..0....3..3..0..0....2..2..2..0
%e A186553 ..0..2..0..0....0..1..1..1....0..2..3..3....0..0..0..2....0..0..1..2
%e A186553 ..0..0..0..3....2..2..1..2....2..3..0..0....2..2..2..1....0..1..1..1
%K A186553 nonn,tabl
%O A186553 1,2
%A A186553 _R. H. Hardin_ Feb 23 2011