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%I #8 Feb 17 2018 10:26:02
%S 1,18,129,899,6205,43066,298361,2068149,14334327,99354814,688646455,
%T 4773147461,33083623049,229309139316,1589386941041,11016355018433,
%U 76356533603993,529242224053012,3668282443014641,25425590535640541
%N Number of n X 3 0..1 arrays with every element equal to 1, 2, 3, 4, 5 or 7 king-move adjacent elements, with upper left element zero.
%C Column 3 of A299142.
%H R. H. Hardin, <a href="/A299137/b299137.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 6*a(n-1) +8*a(n-2) -12*a(n-3) +8*a(n-4) +7*a(n-5) -4*a(n-6) -2*a(n-7) -7*a(n-8) -5*a(n-9) +2*a(n-10) for n>11.
%F Empirical g.f.: x*(1 + 12*x + 13*x^2 - 7*x^3 - 13*x^4 + 41*x^5 - 41*x^6 - 106*x^7 - 37*x^8 + 14*x^9 + 2*x^10) / ((1 - x)*(1 - 5*x - 13*x^2 - x^3 - 9*x^4 - 16*x^5 - 12*x^6 - 10*x^7 - 3*x^8 + 2*x^9)). - _Colin Barker_, Feb 17 2018
%e Some solutions for n=5:
%e ..0..0..1. .0..0..0. .0..1..1. .0..1..1. .0..0..1. .0..1..1. .0..0..1
%e ..1..0..1. .0..1..0. .0..1..0. .0..0..1. .1..1..0. .1..0..0. .0..0..1
%e ..1..1..0. .0..0..1. .0..1..0. .1..0..0. .0..0..1. .0..1..1. .1..0..1
%e ..1..0..0. .1..1..0. .0..0..0. .1..0..1. .0..1..0. .0..0..1. .0..1..0
%e ..0..1..1. .1..0..1. .0..0..0. .1..1..0. .1..0..1. .1..1..1. .1..0..0
%Y Cf. A299142.
%K nonn
%O 1,2
%A _R. H. Hardin_, Feb 03 2018
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