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Number of n X 2 0..4 arrays with no element equal to another at a city block distance of exactly two, and new values 0..4 introduced in row major order.
1

%I #7 Aug 16 2018 15:13:14

%S 2,7,33,273,2433,21873,196833,1771473,15943233,143489073,1291401633,

%T 11622614673,104603532033,941431788273,8472886094433,76255974849873,

%U 686303773648833,6176733962839473,55590605665555233,500315450989997073

%N Number of n X 2 0..4 arrays with no element equal to another at a city block distance of exactly two, and new values 0..4 introduced in row major order.

%C Column 2 of A222944.

%H R. H. Hardin, <a href="/A222940/b222940.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 10*a(n-1) - 9*a(n-2) for n>4.

%F Conjectures from _Colin Barker_, Aug 16 2018: (Start)

%F G.f.: x*(2 - 13*x - 19*x^2 + 6*x^3) / ((1 - x)*(1 - 9*x)).

%F a(n) = 3 + 10*3^(2*n-5) for n>2

%F (End)

%e Some solutions for n=3:

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

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

%e ..1..4....4..0....4..4....2..2....1..0....2..0....2..3....3..3....1..0....2..3

%Y Cf. A222944.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 09 2013