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%I #8 Aug 16 2018 13:23:06
%S 3,34,991,84521,11047723,1639681049,251412693667,38863548783281,
%T 6019757701002763,932903107051648169,144593771181391763827,
%U 22411792379084676340961,3473818375479216866296603
%N Number of n X 3 0..7 arrays with no element equal to another at a city block distance of exactly two, and new values 0..7 introduced in row major order.
%C Column 3 of A222894.
%H R. H. Hardin, <a href="/A222892/b222892.txt">Table of n, a(n) for n = 1..108</a>
%F Empirical: a(n) = 211*a(n-1) - 9385*a(n-2) + 110913*a(n-3) - 253890*a(n-4) for n>6.
%F Conjectures from _Colin Barker_, Aug 16 2018: (Start)
%F G.f.: x*(3 - 599*x + 21972*x^2 - 138229*x^3 - 495045*x^4 + 558558*x^5) / ((1 - 3*x)*(1 - 14*x)*(1 - 39*x)*(1 - 155*x)).
%F a(n) = 3^n + 5*2^(n-1)*7^(n-2) + 14*5^(n-3)*31^(n-2) + 10*39^(n-2) for n>2.
%F (End)
%e Some solutions for n=3:
%e ..0..1..2....0..1..1....0..1..2....0..1..2....0..1..2....0..1..2....0..1..2
%e ..3..4..5....0..2..2....3..4..5....3..4..2....2..1..0....3..1..2....3..4..5
%e ..2..0..5....3..3..0....1..6..7....2..0..3....3..4..4....2..0..4....1..4..5
%Y Cf. A222894.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 08 2013
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