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A232161 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, vertically or antidiagonally, and no adjacent values equal.

%I A232161 #6 Jul 23 2025 06:56:27
%S A232161 1,2,2,4,18,4,8,62,62,8,14,218,290,218,14,26,746,1284,1284,746,26,48,
%T A232161 2600,5902,7770,5902,2600,48,88,9004,27086,46702,46702,27086,9004,88,
%U A232161 162,31262,124436,286770,382996,286770,124436,31262,162,298,108492,572080
%N A232161 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, vertically or antidiagonally, and no adjacent values equal.
%C A232161 Table starts
%C A232161 ...1......2........4.........8..........14...........26.............48
%C A232161 ...2.....18.......62.......218.........746.........2600...........9004
%C A232161 ...4.....62......290......1284........5902........27086.........124436
%C A232161 ...8....218.....1284......7770.......46702.......286770........1767266
%C A232161 ..14....746.....5902.....46702......382996......3183932.......26694774
%C A232161 ..26...2600....27086....286770.....3183932.....36275078......415332300
%C A232161 ..48...9004...124436...1767266....26694774....415332300.....6564512068
%C A232161 ..88..31262...572080..10830650...223026806...4764939084...103384156384
%C A232161 .162.108492..2629946..66701686..1869037596..54785401618..1636124088162
%C A232161 .298.376566.12090710.410364610.15673051556.629979277720.25973583237174
%H A232161 R. H. Hardin, <a href="/A232161/b232161.txt">Table of n, a(n) for n = 1..199</a>
%F A232161 Empirical for column k:
%F A232161 k=1: a(n) = a(n-1) +a(n-2) +a(n-3) for n>4
%F A232161 k=2: [order 10] for n>11
%F A232161 k=3: [order 30] for n>33
%F A232161 k=4: [order 94] for n>97
%e A232161 Some solutions for n=4 k=4
%e A232161 ..3..0..2..3....1..3..2..0....2..3..1..2....3..1..2..3....1..0..3..0
%e A232161 ..2..1..0..1....2..0..1..2....1..2..0..3....2..0..1..2....2..1..2..1
%e A232161 ..0..2..3..2....3..2..0..3....0..3..1..2....1..3..0..1....3..0..3..2
%e A232161 ..3..0..1..3....1..3..2..1....2..0..3..1....2..1..2..3....1..2..0..1
%Y A232161 Column 1 is A135491(n-1)
%K A232161 nonn,tabl
%O A232161 1,2
%A A232161 _R. H. Hardin_, Nov 19 2013