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A260170 Number of (n+2) X (1+2) 0..1 arrays with each 3 X 3 subblock having clockwise perimeter pattern 00000001 00000101 or 00010001. 1

%I #7 Dec 28 2018 09:06:45

%S 40,74,183,409,950,2221,5235,12063,28230,65845,153721,357676,835423,

%T 1947580,4542768,10590805,24709416,57615880,134380567,313384529,

%U 730933689,1704584262,3975550976,9271665730,21623741651,50430265244

%N Number of (n+2) X (1+2) 0..1 arrays with each 3 X 3 subblock having clockwise perimeter pattern 00000001 00000101 or 00010001.

%H R. H. Hardin, <a href="/A260170/b260170.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) + 2*a(n-2) + 2*a(n-3) + 6*a(n-4) - 8*a(n-5) - 3*a(n-6) - 4*a(n-7) - 10*a(n-8) - 4*a(n-9) + 8*a(n-10) for n>11.

%F Empirical g.f.: x*(40 + 34*x + 29*x^2 - 2*x^3 - 213*x^4 - 37*x^5 - 90*x^6 - 122*x^7 + 72*x^8 + 152*x^9 - 60*x^10) / (1 - x - 2*x^2 - 2*x^3 - 6*x^4 + 8*x^5 + 3*x^6 + 4*x^7 + 10*x^8 + 4*x^9 - 8*x^10). - _Colin Barker_, Dec 28 2018

%e Some solutions for n=4:

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

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

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

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

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

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

%Y Column 1 of A260177.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jul 17 2015

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Last modified April 24 08:48 EDT 2024. Contains 371930 sequences. (Running on oeis4.)