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Number of length n+2 0..3 arrays with no three consecutive terms having the sum of any two elements equal to twice the third.
1

%I #9 Nov 08 2018 19:08:42

%S 48,148,460,1436,4488,14040,43940,137532,430508,1347652,4218704,

%T 13206360,41341772,129418260,405137308,1268262348,3970233208,

%U 12428621208,38907193300,121797075276,381279818252,1193577924020,3736437636672

%N Number of length n+2 0..3 arrays with no three consecutive terms having the sum of any two elements equal to twice the third.

%H R. H. Hardin, <a href="/A248456/b248456.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: 4*x*(12 + 13*x + 5*x^2 - 30*x^3 - 53*x^4 - 16*x^5) / (1 - 2*x - 3*x^2 - 4*x^3 + 3*x^4 + 12*x^5 + 4*x^6). - _Colin Barker_, Nov 08 2018

%e Some solutions for n=6:

%e ..0....0....0....1....0....2....2....2....2....3....3....1....2....2....0....2

%e ..3....1....3....1....3....3....1....0....3....0....3....1....2....2....3....2

%e ..1....3....1....3....3....0....1....3....3....3....1....0....3....0....2....1

%e ..3....3....3....0....1....0....3....0....2....0....1....1....0....2....0....1

%e ..1....1....0....0....0....3....1....2....3....1....2....0....3....3....0....2

%e ..3....0....3....3....3....3....3....3....3....0....1....0....0....0....2....2

%e ..1....1....0....0....1....0....1....0....2....3....2....2....0....3....0....1

%e ..1....3....2....1....0....0....3....0....2....0....2....2....1....0....2....1

%Y Column 3 of A248461.

%K nonn

%O 1,1

%A _R. H. Hardin_, Oct 06 2014