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 A228791 Number of n X 3 binary arrays with top left element equal to 1 and no two ones adjacent horizontally or nw-se. 1

%I #12 Sep 13 2018 06:07:56

%S 2,8,36,156,672,2892,12444,53544,230388,991308,4265376,18352956,

%T 78968652,339784392,1462016004,6290726844,27067586208,116465750508,

%U 501125993916,2156232718056,9277785608532,39920229888492,171767792616864

%N Number of n X 3 binary arrays with top left element equal to 1 and no two ones adjacent horizontally or nw-se.

%H R. H. Hardin, <a href="/A228791/b228791.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) - 3*a(n-2) for n>3.

%F Conjectures from _Colin Barker_, Sep 13 2018: (Start)

%F G.f.: 2*x*(1 - x + x^2) / (1 - 5*x + 3*x^2).

%F a(n) = -(2^(1-n)*((-11+sqrt(13))*(5+sqrt(13))^n + (5-sqrt(13))^n*(11+sqrt(13)))) / (9*sqrt(13)) for n>1.

%F (End)

%e Some solutions for n=4:

%e ..1..0..0....1..0..0....1..0..0....1..0..1....1..0..1....1..0..1....1..0..1

%e ..1..0..0....0..0..0....0..0..0....0..0..1....0..0..0....0..0..1....1..0..0

%e ..1..0..1....0..0..0....1..0..1....0..1..0....0..1..0....0..0..1....0..0..1

%e ..0..0..1....1..0..0....0..0..1....0..1..0....0..0..0....0..0..0....1..0..1

%Y Column 3 of A228796.

%K nonn

%O 1,1

%A _R. H. Hardin_, Sep 04 2013

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Last modified September 23 21:37 EDT 2023. Contains 365554 sequences. (Running on oeis4.)