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Number of (n+1) X (1+1) 0..1 arrays with each 2 X 2 subblock having clockwise pattern 0000 0001 0011 0101 or 1111.
1

%I #8 Dec 25 2018 11:15:21

%S 12,38,120,380,1204,3816,12096,38344,121552,385328,1221520,3872320,

%T 12275584,38914656,123362816,391070784,1239728192,3930045568,

%U 12458584320,39494789760,125201899264,396900848896,1258210017536,3988634573824

%N Number of (n+1) X (1+1) 0..1 arrays with each 2 X 2 subblock having clockwise pattern 0000 0001 0011 0101 or 1111.

%H R. H. Hardin, <a href="/A259517/b259517.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: 2*x*(2 + x)*(3 - 4*x) / (1 - 4*x + 2*x^2 + 2*x^3). - _Colin Barker_, Dec 25 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 1 of A259524.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jun 29 2015