%I #6 May 11 2023 14:36:19
%S 3,4,9,23,31,184,427,1115,4128,11024,32827,104959,302093,917104,
%T 2804565,8324555,25231517,76267810,228857830,691699768,2085676297,
%U 6280152762,18952185100,57128981249,172189537544,519305913429,1565482526696
%N Number of n X 3 0..1 arrays with every element equal to 0, 1, 3, 4, 5 or 7 king-move adjacent elements, with upper left element zero.
%C Column 3 of A299128.
%H R. H. Hardin, <a href="/A299123/b299123.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = a(n-1) +4*a(n-2) +16*a(n-3) -13*a(n-4) -35*a(n-5) -62*a(n-6) +28*a(n-7) +65*a(n-8) +36*a(n-9) +61*a(n-10) +59*a(n-11) -34*a(n-12) -64*a(n-13) -36*a(n-14) -40*a(n-15) +3*a(n-16) +18*a(n-17) +2*a(n-18) for n>19.
%e Some solutions for n=5
%e ..0..0..0. .0..1..0. .0..1..1. .0..0..0. .0..0..0. .0..1..1. .0..1..0
%e ..0..0..0. .1..1..1. .0..1..1. .0..0..0. .0..0..0. .1..1..1. .0..1..0
%e ..0..1..0. .1..0..1. .0..0..0. .0..0..1. .0..1..0. .1..1..1. .0..0..0
%e ..0..0..0. .1..1..1. .0..1..1. .0..0..0. .0..0..0. .0..0..0. .1..0..1
%e ..0..0..0. .0..1..0. .0..1..1. .0..0..0. .1..0..1. .0..0..0. .1..0..1
%Y Cf. A299128.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 03 2018
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