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A190032 Number of (n+2) X 10 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 09:56:51

%S 1508,423,610,966,1418,1834,2362,3018,3834,5122,6886,9242,12530,16874,

%T 22626,30959,42112,57029,77815,105765,143231,194899,264884,359302,

%U 488708,664381,901953,1226181,1666661,2263458,3076317,4181101,5679774,7718737

%N Number of (n+2) X 10 binary arrays with every 3 X 3 subblock commuting with each horizontal and vertical neighbor 3 X 3 subblock.

%C Column 8 of A190033.

%H R. H. Hardin, <a href="/A190032/b190032.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>16.

%F Empirical g.f.: x*(1508 - 2593*x + 1272*x^2 - 1339*x^3 + 2689*x^4 - 1308*x^5 - 1565*x^6 + 1117*x^7 + 9*x^8 + 4*x^9 - 104*x^10 + 16*x^11 - 68*x^12 - 76*x^13 + 361*x^15) / ((1 - x)*(1 - x - x^3 + x^4 - x^6)). - _Colin Barker_, May 03 2018

%e Some solutions for 4 X 10:

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

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

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

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