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Number of (n+1) X 2 0..2 arrays with no 2 X 2 subblock summing to less than 4.
2

%I #9 Feb 27 2018 10:38:26

%S 50,336,2167,14180,92429,603249,3935721,25680486,167558680,1093290051,

%T 7133495992,46544663377,303694712145,1981548052649,12929209539882,

%U 84360538526896,550435849841567,3591485193655532,23433731463177813

%N Number of (n+1) X 2 0..2 arrays with no 2 X 2 subblock summing to less than 4.

%C Column 1 of A184564.

%H R. H. Hardin, <a href="/A184556/b184556.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 6*a(n-1) + 7*a(n-2) - 23*a(n-3) - 4*a(n-4) + 12*a(n-5).

%F Empirical g.f.: x*(50 + 36*x - 199*x^2 - 24*x^3 + 108*x^4) / ((1 + 2*x)*(1 - 8*x + 9*x^2 + 5*x^3 - 6*x^4)). - _Colin Barker_, Feb 27 2018

%e Some solutions for 3 X 2:

%e ..2..1....1..2....0..0....1..2....0..2....1..0....2..0....2..0....2..0....2..2

%e ..2..1....2..0....2..2....1..1....2..1....2..2....1..1....1..2....1..2....2..1

%e ..1..0....2..0....0..0....2..2....0..2....0..2....2..1....0..1....2..2....1..0

%Y Cf. A184564.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 17 2011