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Number of 3Xn arrays containing n copies of 0..3-1 with no equal vertical neighbors and new values introduced sequentially from 0.
2

%I #11 Mar 08 2023 03:21:34

%S 1,7,56,495,4686,46456,475392,4976271,52977890,571434402,6228357312,

%T 68468597544,758063599632,8443936740960,94545206802816,

%U 1063391499647631,12007844534804202,136068111377744686,1546682224461979920

%N Number of 3Xn arrays containing n copies of 0..3-1 with no equal vertical neighbors and new values introduced sequentially from 0.

%C Row 3 of A265232.

%H R. H. Hardin, <a href="/A265233/b265233.txt">Table of n, a(n) for n = 1..106</a>

%F Conjecture: n^2*a(n) +(-19*n^2+19*n-6)*a(n-1) +96*(n-1)^2*a(n-2) -144*(n-1)*(n-2)*a(n-3)=0. - _R. J. Mathar_, Dec 08 2015

%F Conjecture: a(n) ~ 2^(2*n - 1) * 3^(n - 1/2) / (Pi*n). - _Vaclav Kotesovec_, Mar 08 2023

%e Some solutions for n=4

%e ..0..1..0..2....0..1..2..2....0..1..0..0....0..1..1..2....0..1..1..2

%e ..2..0..2..0....2..0..1..0....2..2..2..2....1..2..2..0....2..0..0..0

%e ..1..1..1..2....0..1..2..1....1..1..0..1....0..0..1..2....1..1..2..2

%Y Cf. A265232.

%K nonn

%O 1,2

%A _R. H. Hardin_, Dec 06 2015