A268735 - OEIS

%I #8 Jan 14 2019 09:01:55

%S 2,15,80,396,1788,7831,33170,137868,563486,2275119,9091772,36031648,

%T 141793168,554669335,2158604934,8363066408,32273565050,124112115647,

%U 475807505288,1819019281732,6936664653476,26392068734023,100206016839642

%N Number of n X 3 binary arrays with some 1 horizontally or vertically adjacent to some other 1 exactly once.

%H R. H. Hardin, <a href="/A268735/b268735.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) + 8*a(n-2) - 24*a(n-3) - 38*a(n-4) + 4*a(n-5) + 12*a(n-6) - a(n-8).

%F Empirical g.f.: x*(2 + 7*x + 4*x^2 + 4*x^3 - 7*x^5 + 2*x^6) / (1 - 2*x - 6*x^2 + x^4)^2. - _Colin Barker_, Jan 14 2019

%e Some solutions for n=4:

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

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

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

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

%Y Column 3 of A268740.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 12 2016