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A186472 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock commuting with each of its horizontal and vertical 2X2 subblock neighbors.

%I A186472 #7 Jul 22 2025 10:20:54
%S A186472 81,83,83,277,129,277,367,243,243,367,966,562,942,562,966,1321,903,
%T A186472 1203,1203,903,1321,3078,1754,3190,3186,3190,1754,3078,4553,2937,4023,
%U A186472 4875,4875,4023,2937,4553,10028,5790,9982,9834,13278,9834,9982,5790,10028
%N A186472 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock commuting with each of its horizontal and vertical 2X2 subblock neighbors.
%C A186472 Table starts
%C A186472 ....81....83...277....367....966...1321...3078....4553...10028...15650...32786
%C A186472 ....83...129...243....562....903...1754...2937....5790....9993...19236...33546
%C A186472 ...277...243...942...1203...3190...4023...9982...13985...32390...48553..105436
%C A186472 ...367...562..1203...3186...4875...9834..14883...31866...51057..105398..174289
%C A186472 ...966...903..3190...4875..13278..16083..40626...52755..129102..182841..418022
%C A186472 ..1321..1754..4023...9834..16083..34314..49407..109950..159879..350418..540777
%C A186472 ..3078..2937..9982..14883..40626..49407.136086..170811..431658..564459.1356918
%C A186472 ..4553..5790.13985..31866..52755.109950.170811..399018..570183.1266414.1812423
%C A186472 .10028..9993.32390..51057.129102.159879.431658..570183.1537038.1966755.4790010
%C A186472 .15650.19236.48553.105398.182841.350418.564459.1266414.1966755.4607034.6457959
%H A186472 R. H. Hardin, <a href="/A186472/b186472.txt">Table of n, a(n) for n = 1..473</a>
%F A186472 Empirical, for every column: a(n)=2*a(n-1)+a(n-2)-4*a(n-3)+4*a(n-4)-2*a(n-5) for n>k+9
%e A186472 Some solutions for 4X3
%e A186472 ..1..1..0....2..1..1....2..0..0....2..0..0....0..2..1....0..1..0....2..0..1
%e A186472 ..2..0..1....1..1..0....0..2..0....0..0..0....0..0..2....1..0..1....0..2..0
%e A186472 ..0..2..0....1..0..1....1..0..2....0..0..0....0..0..0....0..1..0....2..0..2
%e A186472 ..2..0..2....0..1..2....0..1..1....2..0..0....1..0..0....0..0..1....0..2..1
%K A186472 nonn,tabl
%O A186472 1,1
%A A186472 _R. H. Hardin_ Feb 22 2011