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Number of (n+1) X (3+1) 0..1 arrays with no 2 X 2 subblock having zero or two 1s.
1

%I #8 Nov 27 2018 09:01:42

%S 49,191,758,3089,12503,50912,206715,840931,3417338,13896689,56488843,

%T 229680232,933724343,3796257055,15433585490,62747204885,255100769239,

%U 1037135769960,4216531992291,17142642411675,69694499491242

%N Number of (n+1) X (3+1) 0..1 arrays with no 2 X 2 subblock having zero or two 1s.

%H R. H. Hardin, <a href="/A251214/b251214.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) + 17*a(n-2) - 20*a(n-3) - 85*a(n-4) + 68*a(n-5) + 146*a(n-6) - 84*a(n-7) - 56*a(n-8) + 24*a(n-9).

%F Empirical g.f.: x*(49 + 93*x - 457*x^2 - 694*x^3 + 1424*x^4 + 1456*x^5 - 1592*x^6 - 692*x^7 + 384*x^8) / (1 - 2*x - 17*x^2 + 20*x^3 + 85*x^4 - 68*x^5 - 146*x^6 + 84*x^7 + 56*x^8 - 24*x^9). - _Colin Barker_, Nov 27 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 3 of A251219.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 30 2014