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A183399 Half the number of n X 3 binary arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors. 1

%I

%S 4,2,6,32,110,450,1680,6498,24794,95048,364030,1394450,5342640,

%T 20467202,78415506,300419072,1150965830,4409544050,16893761040,

%U 64722982898,247965235594,949998793608,3639613683310,13944005214050,53421954623280

%N Half the number of n X 3 binary arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors.

%C Column 3 of A183402.

%H R. H. Hardin, <a href="/A183399/b183399.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 5*a(n-1) - 23*a(n-3) + 15*a(n-4) + 40*a(n-5) - 46*a(n-6) + 20*a(n-8) - 8*a(n-9) for n>10.

%F Empirical g.f.: 2*x*(2 - 9*x - 2*x^2 + 47*x^3 - 32*x^4 - 76*x^5 + 90*x^6 - 40*x^8 + 16*x^9) / ((1 - 5*x + 5*x^2 - 2*x^3)*(1 - 5*x^2 + 10*x^4 - 4*x^6)). - _Colin Barker_, Mar 28 2018

%e Some solutions with a(1,1)=0 for 4 X 3:

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

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

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

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

%Y Cf. A183402.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 04 2011

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Last modified August 11 03:41 EDT 2022. Contains 356046 sequences. (Running on oeis4.)