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Number of n X 2 binary arrays with every one adjacent to another one horizontally, diagonally, antidiagonally or vertically.
2

%I #11 Mar 03 2018 05:35:40

%S 2,12,50,188,724,2820,10960,42544,165176,641376,2490416,9669968,

%T 37547296,145791744,566092192,2198069056,8534842304,33139784256,

%U 128677866752,499640952320,1940046781312,7532972421120,29249641835776,113572903188736

%N Number of n X 2 binary arrays with every one adjacent to another one horizontally, diagonally, antidiagonally or vertically.

%C Column 2 of A202795.

%H R. H. Hardin, <a href="/A202789/b202789.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) - 2*a(n-2) + 6*a(n-3).

%F Empirical g.f.: 2*x*(1 + 2*x + 3*x^2) / (1 - 4*x + 2*x^2 - 6*x^3). - _Colin Barker_, Mar 03 2018

%e Some solutions for n=5:

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

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

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

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

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

%Y Cf. A202795.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 24 2011