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A190029 Number of (n+2) X 7 binary arrays with every 3 X 3 subblock commuting with each horizontal and vertical neighbor 3 X 3 subblock. 1

%I

%S 616,235,362,578,834,970,1162,1418,1802,2446,3314,4446,6199,8432,

%T 11313,15459,20953,28227,38519,52392,70926,96624,131397,178105,242269,

%U 329381,446962,607697,826153,1121786,1524737,2072521,2815063,3825658,5199542

%N Number of (n+2) X 7 binary arrays with every 3 X 3 subblock commuting with each horizontal and vertical neighbor 3 X 3 subblock.

%C Column 5 of A190033.

%H R. H. Hardin, <a href="/A190029/b190029.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>13.

%F Empirical g.f.: x*(616 - 997*x + 508*x^2 - 527*x^3 + 1037*x^4 - 628*x^5 - 649*x^6 + 405*x^7 + 121*x^8 - 12*x^9 - 96*x^10 + 169*x^12) / ((1 - x)*(1 - x - x^3 + x^4 - x^6)). - _Colin Barker_, May 03 2018

%e Some solutions for 4 X 7:

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

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

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

%e ..0..1..0..0..0..0..0....1..1..0..0..0..0..0....0..1..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 September 21 09:52 EDT 2021. Contains 347597 sequences. (Running on oeis4.)