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A183336 Number of n X 4 binary arrays with each 1 adjacent to exactly one 1 vertically and one 1 horizontally. 1

%I #9 Mar 27 2018 09:36:44

%S 1,4,7,12,26,51,97,193,380,741,1456,2860,5605,10997,21581,42332,83047,

%T 162936,319650,627099,1230289,2413641,4735192,9289761,18225136,

%U 35754992,70146009,137616081,269982313,529665276,1039124759,2038608652,3999447882

%N Number of n X 4 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 4 of A183342.

%H R. H. Hardin, <a href="/A183336/b183336.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = a(n-1) + a(n-2) + 2*a(n-3) - a(n-5).

%F Empirical g.f.: x*(1 + x)^2*(1 + x - x^2) / (1 - x - x^2 - 2*x^3 + x^5). - _Colin Barker_, Mar 27 2018

%e Some solutions for 5 X 4:

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

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

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

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

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

%Y Cf. A183342.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 04 2011

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Last modified July 21 22:27 EDT 2024. Contains 374478 sequences. (Running on oeis4.)