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A231103 Number of n X 3 0..3 arrays x(i,j) with each element horizontally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, no adjacent elements equal, and upper left element zero. 1

%I

%S 0,2,8,42,208,1042,5208,26042,130208,651042,3255208,16276042,81380208,

%T 406901042,2034505208,10172526042,50862630208,254313151042,

%U 1271565755208,6357828776042,31789143880208,158945719401042,794728597005208

%N Number of n X 3 0..3 arrays x(i,j) with each element horizontally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, no adjacent elements equal, and upper left element zero.

%H R. H. Hardin, <a href="/A231103/b231103.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) + 5*a(n-2).

%F Conjectures from _Colin Barker_, Sep 26 2018: (Start)

%F G.f.: 2*x^2 / ((1 + x)*(1 - 5*x)).

%F a(n) = (5^n + 5) / 15 for n even.

%F a(n) = (5^n - 5) / 15 for n odd.

%F (End)

%e Some solutions for n=4:

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

%e ..2..3..1....0..3..0....2..3..0....2..3..0....0..3..2....0..3..2....0..3..1

%e ..1..2..1....2..1..0....0..1..0....0..1..0....2..0..3....2..3..2....1..2..3

%e ..3..0..3....0..3..2....2..3..2....2..3..2....1..2..1....0..1..0....1..0..3

%Y Column 3 of A231108.

%K nonn

%O 1,2

%A _R. H. Hardin_, Nov 03 2013

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Last modified October 16 10:19 EDT 2021. Contains 348041 sequences. (Running on oeis4.)