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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 or 00000101.
1

%I #11 Dec 26 2018 12:15:41

%S 32,49,104,201,376,745,1494,2897,5610,11065,21780,42461,82984,162977,

%T 319406,624529,1222926,2397205,4694532,9189573,17999120,35259025,

%U 69046594,135207885,264815462,518655749,1015714340,1989176813,3895806716

%N Number of (n+2) X (1+2) 0..1 arrays with each 3 X 3 subblock having clockwise perimeter pattern 00000001 or 00000101.

%H R. H. Hardin, <a href="/A259765/b259765.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: x*(32 + 49*x + 72*x^2 + 88*x^3 - 18*x^4 - 22*x^5 + 26*x^6 - 29*x^7 + 6*x^8) / (1 - x^2 - 2*x^3 - 6*x^4 - 2*x^5 + x^6 - 2*x^7 + x^8). - _Colin Barker_, Dec 26 2018

%e Some solutions for n=4:

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

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

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

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

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

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

%Y Column 1 of A259770.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jul 04 2015