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A260364 Number of (n+2) X (2+2) 0..1 arrays with each 3 X 3 subblock having clockwise perimeter pattern 00000001 00000011 or 00001111. 1

%I #8 Dec 29 2018 07:08:14

%S 78,127,342,700,896,2047,4438,6674,12878,27877,46806,84404,175894,

%T 316729,562556,1122802,2100112,3759241,7255522,13784466,25036860,

%U 47321615,90142076,165956528,310385576,589328265,1095576864,2041368188,3857505346

%N Number of (n+2) X (2+2) 0..1 arrays with each 3 X 3 subblock having clockwise perimeter pattern 00000001 00000011 or 00001111.

%H R. H. Hardin, <a href="/A260364/b260364.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-2) + 5*a(n-3) + 5*a(n-4) - 4*a(n-5) - 6*a(n-6) - 10*a(n-7) - 7*a(n-8) + 4*a(n-9) + 5*a(n-10) + 5*a(n-11) + 3*a(n-12).

%F Empirical g.f.: x*(78 + 127*x + 264*x^2 + 183*x^3 - 471*x^4 - 686*x^5 - 692*x^6 - 443*x^7 + 393*x^8 + 559*x^9 + 428*x^10 + 268*x^11) / ((1 - x)*(1 + x)^2*(1 + x^2)*(1 - x - 5*x^3 + x^4 + 3*x^5 + 2*x^6 + 3*x^7)). - _Colin Barker_, Dec 29 2018

%e Some solutions for n=4:

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

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

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

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

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

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

%Y Column 2 of A260370.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jul 23 2015

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Last modified September 27 20:41 EDT 2023. Contains 365714 sequences. (Running on oeis4.)