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%I #7 Jan 01 2024 18:43:14
%S 108,323,1058,3223,9515,28426,84486,249106,734637,2166526,6380211,
%T 18782449,55296998,162765970,479038288,1409873905,4149367138,
%U 12211531035,35938252497,105765419940,311263342522,916033572652,2695845174863
%N Number of (n+2) X 3 binary arrays avoiding patterns 001 and 010 in rows and columns.
%C Column 1 of A202616.
%H R. H. Hardin, <a href="/A202609/b202609.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 4*a(n-1) -5*a(n-2) +16*a(n-3) -35*a(n-4) +19*a(n-5) -48*a(n-6) +80*a(n-7) +12*a(n-8) +52*a(n-9) -92*a(n-10) -54*a(n-11) -52*a(n-12) +76*a(n-13) +43*a(n-14) +32*a(n-15) -27*a(n-16) -16*a(n-17) -11*a(n-18) +5*a(n-19) +2*a(n-21).
%e Some solutions for n=3
%e ..1..1..0....1..0..1....1..0..1....1..1..0....1..1..1....0..1..1....0..1..1
%e ..1..1..1....1..1..1....1..1..1....1..1..1....1..1..1....1..1..1....1..1..0
%e ..1..1..1....1..1..1....0..1..1....0..1..1....0..1..1....1..1..0....1..1..1
%e ..0..1..1....0..0..0....1..1..1....1..0..0....0..0..0....1..1..0....1..1..1
%e ..0..1..1....1..0..1....1..0..1....1..1..0....0..0..0....1..0..0....0..1..1
%Y Cf. A202616.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 21 2011
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