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%I #8 Mar 22 2018 09:46:59
%S 4,18,45,116,293,735,1844,4626,11611,29151,73200,183828,461671,
%T 1159483,2912066,7313756,18368803,46134069,115867838,291007480,
%U 730878941,1835636845,4610288394,11578956554,29081095145,73038541289,183439739500
%N Number of n X 3 0..1 arrays with no element equal to more than two of its horizontal, vertical and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.
%C Column 3 of A280604.
%H R. H. Hardin, <a href="/A280599/b280599.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 4*a(n-1) - 3*a(n-2) - 3*a(n-3) + 2*a(n-4) + 3*a(n-5) - 2*a(n-6) for n>8.
%F Empirical g.f.: x*(4 + 2*x - 15*x^2 + 2*x^3 + 10*x^4 - 2*x^5 - 5*x^6 + 3*x^7) / ((1 - x)^3*(1 - x - 3*x^2 - 2*x^3)). - _Colin Barker_, Mar 22 2018
%e Some solutions for n=4:
%e ..0..1..0. .0..0..0. .0..0..1. .0..0..0. .0..1..1. .0..1..0. .0..1..0
%e ..1..0..1. .1..1..1. .1..1..0. .1..1..0. .1..0..1. .0..1..0. .1..0..0
%e ..1..0..1. .0..0..1. .0..0..1. .1..0..1. .0..1..0. .1..0..1. .1..1..1
%e ..0..1..0. .1..0..0. .1..1..0. .0..1..0. .0..1..1. .0..1..0. .0..0..0
%Y Cf. A280604.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 06 2017
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