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Number of (n+2) X (1+2) 0..1 arrays with each 3 X 3 subblock having clockwise perimeter pattern 00000001 00000011 or 00001001.
1

%I #8 Dec 29 2018 07:08:26

%S 48,104,274,560,966,2300,4762,8252,17470,38160,71698,142360,304646,

%T 599716,1172578,2447716,4949782,9718248,19837162,40474736,80338222,

%U 161965772,330213194,661573644,1327566094,2695382016,5430701122

%N Number of (n+2) X (1+2) 0..1 arrays with each 3 X 3 subblock having clockwise perimeter pattern 00000001 00000011 or 00001001.

%H R. H. Hardin, <a href="/A260287/b260287.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-3) + 5*a(n-4) + 2*a(n-5) + 8*a(n-6) + 8*a(n-7) - 4*a(n-8) - 8*a(n-9) for n>10.

%F Empirical g.f.: 2*x*(24 + 52*x + 137*x^2 + 184*x^3 + 155*x^4 + 294*x^5 + 280*x^6 - 88*x^7 - 256*x^8 - 96*x^9) / (1 - 4*x^3 - 5*x^4 - 2*x^5 - 8*x^6 - 8*x^7 + 4*x^8 + 8*x^9). - _Colin Barker_, Dec 29 2018

%e Some solutions for n=4:

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

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

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

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

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

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

%Y Column 1 of A260294.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jul 22 2015