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A232295 T(n,k)=Number of nXk 0..2 arrays with every 0 next to a 1 and every 1 next to a 2 horizontally or antidiagonally.

%I A232295 #6 Jul 23 2025 07:16:09
%S A232295 1,3,1,7,15,1,15,97,73,1,33,587,1313,355,1,73,3615,20563,17759,1727,1,
%T A232295 161,22387,336079,718483,240241,8401,1,355,138505,5546705,31119789,
%U A232295 25116353,3249889,40867,1,783,856719,91293443,1370434057,2885285507
%N A232295 T(n,k)=Number of nXk 0..2 arrays with every 0 next to a 1 and every 1 next to a 2 horizontally or antidiagonally.
%C A232295 Table starts
%C A232295 .1......3..........7.............15.................33.....................73
%C A232295 .1.....15.........97............587...............3615..................22387
%C A232295 .1.....73.......1313..........20563.............336079................5546705
%C A232295 .1....355......17759.........718483...........31119789.............1370434057
%C A232295 .1...1727.....240241.......25116353.........2885285507...........339565321435
%C A232295 .1...8401....3249889......877968487.......267483142619.........84130295708483
%C A232295 .1..40867...43963319....30690409685.....24797475083765......20843967523877175
%C A232295 .1.198799..594719777..1072818688305...2298890419506403....5164265865545602229
%C A232295 .1.967065.8045152705.37501616113029.213122398219612007.1279489656786836660869
%H A232295 R. H. Hardin, <a href="/A232295/b232295.txt">Table of n, a(n) for n = 1..199</a>
%F A232295 Empirical for column k:
%F A232295 k=1: a(n) = a(n-1)
%F A232295 k=2: a(n) = 4*a(n-1) +4*a(n-2) +a(n-3)
%F A232295 k=3: a(n) = 12*a(n-1) +20*a(n-2) +9*a(n-3)
%F A232295 k=4: [order 10]
%F A232295 k=5: [order 13] for n>14
%F A232295 k=6: [order 37] for n>38
%F A232295 Empirical for row n:
%F A232295 n=1: a(n) = 2*a(n-1) +a(n-3)
%F A232295 n=2: [order 9]
%F A232295 n=3: [order 31]
%e A232295 Some solutions for n=3 k=4
%e A232295 ..2..2..2..1....2..1..2..2....0..1..0..1....2..2..2..2....1..2..1..0
%e A232295 ..2..1..0..0....1..2..2..1....2..2..2..0....1..1..2..0....2..0..2..2
%e A232295 ..0..0..1..2....1..0..2..2....2..2..1..2....2..2..1..2....2..2..1..0
%Y A232295 Row 1 is A193641
%K A232295 nonn,tabl
%O A232295 1,2
%A A232295 _R. H. Hardin_, Nov 22 2013