%I #4 Jan 15 2018 08:27:31
%S 3,4,5,17,12,100,219,498,1999,4953,13928,45164,120865,355474,1065723,
%T 2987665,8792232,25703174,73648001,215508142,625811209,1809121989,
%U 5271819208,15292192284,44347119815,128947618162,374125557341
%N Number of nX3 0..1 arrays with every element equal to 0, 1, 3, 4 or 5 king-move adjacent elements, with upper left element zero.
%C Column 3 of A298230.
%H R. H. Hardin, <a href="/A298225/b298225.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = a(n-1) +4*a(n-2) +13*a(n-3) -14*a(n-4) -29*a(n-5) -23*a(n-6) +29*a(n-7) +56*a(n-8) -30*a(n-9) -7*a(n-10) +41*a(n-11) +2*a(n-12) -26*a(n-13) -12*a(n-14) -15*a(n-15) -7*a(n-16) +16*a(n-17) +2*a(n-18) for n>19
%e Some solutions for n=7
%e ..0..1..1. .0..1..0. .0..1..0. .0..0..1. .0..0..1. .0..1..0. .0..0..1
%e ..0..1..1. .0..1..0. .0..1..0. .0..0..1. .0..0..0. .0..1..0. .0..0..1
%e ..1..1..0. .1..1..1. .0..0..0. .1..1..1. .1..0..1. .0..0..0. .1..1..1
%e ..1..1..0. .0..1..0. .1..0..1. .1..1..0. .0..0..1. .1..0..1. .1..1..0
%e ..1..0..0. .1..1..0. .0..1..0. .0..1..0. .0..1..1. .0..1..0. .0..0..1
%e ..1..1..0. .0..1..1. .1..1..1. .1..1..1. .0..0..1. .1..1..1. .0..0..0
%e ..1..1..0. .0..1..1. .1..1..0. .1..1..0. .0..0..1. .0..1..1. .1..0..1
%Y Cf. A298230.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 15 2018
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