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A232156 Number of nX3 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 A232156 #6 Jul 23 2025 06:55:50
%S A232156 4,62,290,1284,5902,27086,124436,572080,2629946,12090710,55591878,
%T A232156 255589946,1175154022,5403111082,24842308392,114220099740,
%U A232156 525160514282,2414582116408,11101765510580,51043677955498,234688597761528
%N A232156 Number of nX3 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 A232156 Column 3 of A232161
%H A232156 R. H. Hardin, <a href="/A232156/b232156.txt">Table of n, a(n) for n = 1..210</a>
%F A232156 Empirical: a(n) = 8*a(n-1) -12*a(n-2) -33*a(n-3) +40*a(n-4) +286*a(n-5) -545*a(n-6) -642*a(n-7) +2651*a(n-8) -1783*a(n-9) -2378*a(n-10) +4407*a(n-11) -1301*a(n-12) -2857*a(n-13) +3373*a(n-14) +157*a(n-15) -2558*a(n-16) +366*a(n-17) +1084*a(n-18) +818*a(n-19) -2988*a(n-20) -2028*a(n-21) +2529*a(n-22) +1294*a(n-23) +328*a(n-24) +582*a(n-25) -122*a(n-26) -180*a(n-27) +47*a(n-28) +21*a(n-29) -3*a(n-30) for n>33
%e A232156 Some solutions for n=7
%e A232156 ..1..2..3....1..2..3....0..1..2....1..2..3....2..1..0....0..3..1....2..1..2
%e A232156 ..3..1..0....3..1..2....2..0..3....3..0..1....3..2..1....1..2..0....3..0..3
%e A232156 ..0..3..2....2..0..3....3..2..1....1..2..0....1..0..2....0..3..2....1..2..1
%e A232156 ..2..0..1....3..1..2....1..0..3....0..3..2....2..3..0....2..0..3....3..0..2
%e A232156 ..1..3..0....2..3..0....3..2..1....2..0..3....1..2..1....1..2..0....2..3..0
%e A232156 ..0..2..1....1..2..1....0..3..0....3..1..2....0..3..0....3..1..3....0..1..2
%e A232156 ..3..0..3....0..3..0....1..2..1....0..3..1....2..1..3....2..0..2....2..3..1
%K A232156 nonn
%O A232156 1,1
%A A232156 _R. H. Hardin_, Nov 19 2013