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%I #8 Mar 22 2018 17:06:46
%S 1,6,2,5,7,14,21,41,70,129,233,428,783,1445,2664,4933,9137,16956,
%T 31495,58557,108952,202837,377797,703972,1312155,2446433,4562176,
%U 8509137,15873089,29613308,55252631,103098397,192387744,359025085,670023141
%N Number of n X 3 0..1 arrays with every element equal to 0, 2, 3 or 6 king-move adjacent elements, with upper left element zero.
%C Column 3 of A297986.
%H R. H. Hardin, <a href="/A297981/b297981.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = a(n-1) + 2*a(n-2) + a(n-3) - a(n-4) - 4*a(n-6) - 8*a(n-7) - 2*a(n-8) + 4*a(n-9) + 6*a(n-10) + 2*a(n-11) for n>13.
%F Empirical g.f.: x*(1 + 5*x - 6*x^2 - 10*x^3 - 7*x^4 + x^5 - 6*x^6 + 22*x^7 + 38*x^8 + 14*x^9 - 14*x^10 - 16*x^11 - 4*x^12) / ((1 - x)*(1 + x)*(1 - x - x^2 - 2*x^3 - 2*x^5 + 4*x^6 + 6*x^7 + 6*x^8 + 2*x^9)). - _Colin Barker_, Mar 22 2018
%e Some solutions for n=7:
%e ..0..1..1. .0..1..0. .0..1..0. .0..0..1. .0..1..1. .0..1..0. .0..1..0
%e ..0..0..1. .1..1..1. .0..0..0. .0..1..1. .0..0..1. .0..0..0. .0..0..0
%e ..1..0..1. .0..0..0. .0..1..0. .1..0..0. .1..0..1. .0..1..0. .0..1..0
%e ..1..1..1. .1..0..1. .1..1..0. .1..1..0. .1..1..1. .1..1..1. .1..1..0
%e ..1..0..1. .1..1..1. .1..0..0. .0..1..0. .1..0..1. .0..0..0. .0..1..0
%e ..1..0..0. .1..0..1. .0..1..1. .0..0..0. .0..0..1. .1..0..1. .0..0..0
%e ..1..1..0. .0..0..0. .0..0..1. .0..1..0. .0..1..1. .0..0..0. .0..1..0
%Y Cf. A297986.
%K nonn
%O 1,2
%A _R. H. Hardin_, Jan 10 2018
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