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 A190030 Number of (n+2) X 8 binary arrays with every 3 X 3 subblock commuting with each horizontal and vertical neighbor 3 X 3 subblock. 1

%I #8 May 03 2018 09:59:18

%S 880,295,430,670,970,1230,1494,1834,2338,3142,4226,5674,7686,10543,

%T 14268,19361,26383,35721,48439,65943,89488,121506,165332,224537,

%U 304933,414641,563273,765114,1040093,1413201,1919914,2609473,3545793,4817559,6547150

%N Number of (n+2) X 8 binary arrays with every 3 X 3 subblock commuting with each horizontal and vertical neighbor 3 X 3 subblock.

%C Column 6 of A190033.

%H R. H. Hardin, <a href="/A190030/b190030.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 2*a(n-1) -a(n-2) +a(n-3) -2*a(n-4) +a(n-5) +a(n-6) -a(n-7) for n>14.

%F Empirical g.f.: x*(880 - 1465*x + 720*x^2 - 775*x^3 + 1525*x^4 - 760*x^5 - 981*x^6 + 601*x^7 + 69*x^8 + 56*x^9 - 96*x^10 - 60*x^11 + 225*x^13) / ((1 - x)*(1 - x - x^3 + x^4 - x^6)). - _Colin Barker_, May 03 2018

%e Some solutions for 4 X 8:

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

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

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

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

%Y Cf. A190033.

%K nonn

%O 1,1

%A _R. H. Hardin_, May 04 2011

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Last modified April 15 03:58 EDT 2024. Contains 371667 sequences. (Running on oeis4.)