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A232376 T(n,k)=Number of nXk 0..3 arrays with every 0 next to a 1, every 1 next to a 2 and every 2 next to a 3 horizontally, diagonally or antidiagonally, and no adjacent values equal.

%I A232376 #6 Jul 23 2025 07:22:28
%S A232376 1,2,1,4,14,1,8,74,58,1,14,296,586,230,1,26,1130,4404,4550,934,1,48,
%T A232376 4682,32722,63744,36574,3794,1,88,19448,259458,927706,957232,292122,
%U A232376 15354,1,162,79592,2046700,14326374,27133338,14297980,2324142,62266,1,298,326810
%N A232376 T(n,k)=Number of nXk 0..3 arrays with every 0 next to a 1, every 1 next to a 2 and every 2 next to a 3 horizontally, diagonally or antidiagonally, and no adjacent values equal.
%C A232376 Table starts
%C A232376 .1.......2..........4............8..............14.................26
%C A232376 .1......14.........74..........296............1130...............4682
%C A232376 .1......58........586.........4404...........32722.............259458
%C A232376 .1.....230.......4550........63744..........927706...........14326374
%C A232376 .1.....934......36574.......957232........27133338..........825606450
%C A232376 .1....3794.....292122.....14297980.......789866870........47301712998
%C A232376 .1...15354....2324142....213082596.....22946925502......2706080691402
%C A232376 .1...62266...18574882...3180405572....667514680522....154987416800398
%C A232376 .1..252346..148225606..47457708756..19413840326186...8875595994390694
%C A232376 .1.1022806.1182879814.708101568772.564595278464614.508249649361525870
%H A232376 R. H. Hardin, <a href="/A232376/b232376.txt">Table of n, a(n) for n = 1..160</a>
%F A232376 Empirical for column k:
%F A232376 k=1: a(n) = a(n-1)
%F A232376 k=2: a(n) = 2*a(n-1) +7*a(n-2) +6*a(n-3) -2*a(n-4) -3*a(n-5) +2*a(n-6) +a(n-7)
%F A232376 k=3: [order 15]
%F A232376 k=4: [order 22]
%F A232376 k=5: [order 64]
%F A232376 Empirical for row n:
%F A232376 n=1: a(n) = a(n-1) +a(n-2) +a(n-3) for n>4
%F A232376 n=2: [order 8] for n>9
%F A232376 n=3: [order 13] for n>14
%F A232376 n=4: [order 60] for n>61
%e A232376 Some solutions for n=4 k=4
%e A232376 ..0..1..2..1....2..1..2..1....2..3..2..3....2..1..0..3....3..2..0..2
%e A232376 ..0..3..0..1....0..3..2..1....1..0..1..0....2..3..0..3....3..1..3..2
%e A232376 ..2..1..0..3....2..3..2..1....1..2..3..0....2..3..0..3....2..1..0..1
%e A232376 ..3..1..2..3....2..3..2..3....1..2..1..2....0..1..2..1....0..3..2..3
%Y A232376 Row 1 is A135491(n-1)
%K A232376 nonn,tabl
%O A232376 1,2
%A A232376 _R. H. Hardin_, Nov 23 2013