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A183338 Number of n X 6 binary arrays with each 1 adjacent to exactly one 1 vertically and one 1 horizontally. 1

%I #12 Mar 28 2018 08:13:55

%S 1,9,23,51,175,513,1397,4133,12075,34521,100047,290287,838039,2423841,

%T 7016381,20290449,58686583,169784637,491117363,1420584719,4109370831,

%U 11887034385,34384871493,99464136973,287716480627,832264983105

%N Number of n X 6 binary arrays with each 1 adjacent to exactly one 1 vertically and one 1 horizontally.

%C Equivalent to all 1s connected only in 2 X 2 blocks.

%C Column 6 of A183342.

%H R. H. Hardin, <a href="/A183338/b183338.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = a(n-1) + 2*a(n-2) + 9*a(n-3) + 6*a(n-4) - 3*a(n-5) - 10*a(n-6) - 17*a(n-7) - 7*a(n-8) + 12*a(n-9) + 12*a(n-10) - 6*a(n-11).

%F Empirical g.f.: x*(1 + 8*x + 12*x^2 + x^3 - 9*x^4 - 22*x^5 - 26*x^6 + 5*x^7 + 24*x^8 + 6*x^9 - 6*x^10) / (1 - x - 2*x^2 - 9*x^3 - 6*x^4 + 3*x^5 + 10*x^6 + 17*x^7 + 7*x^8 - 12*x^9 - 12*x^10 + 6*x^11). - _Colin Barker_, Mar 27 2018

%e Some solutions for 5 X 6:

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

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

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

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

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

%Y Cf. A183342.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 04 2011

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