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A233733 T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with every 2X2 subblock having the sum of the absolute values of the edge differences equal to 6 and no adjacent elements equal.

%I A233733 #6 Jul 23 2025 08:11:00
%S A233733 40,148,148,556,756,556,2104,3972,3972,2104,7976,21432,29816,21432,
%T A233733 7976,30260,115972,233432,233432,115972,30260,114820,631628,1851404,
%U A233733 2723072,1851404,631628,114820,435720,3435216,14802604,32240288,32240288
%N A233733 T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with every 2X2 subblock having the sum of the absolute values of the edge differences equal to 6 and no adjacent elements equal.
%C A233733 Table starts
%C A233733 ......40.......148.........556..........2104.............7976
%C A233733 .....148.......756........3972.........21432...........115972
%C A233733 .....556......3972.......29816........233432..........1851404
%C A233733 ....2104.....21432......233432.......2723072.........32240288
%C A233733 ....7976....115972.....1851404......32240288........578163016
%C A233733 ...30260....631628....14802604.....389230764......10577526052
%C A233733 ..114820...3435216...118695412....4696134192.....195088215888
%C A233733 ..435720..18733728...953471940...57174669348....3616933627344
%C A233733 .1653488.102007004..7663964828..693181060760...67204709367712
%C A233733 .6274804.556289404.61629254552.8455863542400.1250516988640176
%H A233733 R. H. Hardin, <a href="/A233733/b233733.txt">Table of n, a(n) for n = 1..220</a>
%F A233733 Empirical for column k:
%F A233733 k=1: a(n) = 3*a(n-1) +5*a(n-2) -7*a(n-3) -2*a(n-4)
%F A233733 k=2: [order 12]
%F A233733 k=3: [order 28]
%F A233733 k=4: [order 84]
%e A233733 Some solutions for n=3 k=4
%e A233733 ..2..3..2..3..2....0..2..0..2..0....0..1..0..1..2....0..2..0..1..0
%e A233733 ..0..1..3..1..3....1..0..1..0..1....1..3..1..3..1....2..3..2..3..1
%e A233733 ..2..0..2..0..1....3..1..3..2..0....0..2..0..2..3....3..1..3..1..0
%e A233733 ..3..2..1..2..0....1..0..1..0..1....2..3..2..1..0....1..0..2..0..2
%K A233733 nonn,tabl
%O A233733 1,1
%A A233733 _R. H. Hardin_, Dec 15 2013