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

%I #10 Jan 15 2022 23:12:48

%S 9,21,49,115,269,631,1477,3463,8109,19007,44517,104327,244381,572655,

%T 1341525,3143383,7364173,17254655,40424581,94714855,221903869,

%U 519914127,1218099893,2853948663,6686519981,15666114847,36704297445,85995716871

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

%H R. H. Hardin, <a href="/A251212/b251212.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) + 4*a(n-2) - 2*a(n-3).

%F Empirical g.f.: x*(9 + 12*x - 8*x^2) / (1 - x - 4*x^2 + 2*x^3). - _Colin Barker_, Nov 27 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 1 of A251219.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 30 2014