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

%I #8 Nov 08 2018 19:08:58

%S 6,18,48,96,174,282,432,624,870,1170,1536,1968,2478,3066,3744,4512,

%T 5382,6354,7440,8640,9966,11418,13008,14736,16614,18642,20832,23184,

%U 25710,28410,31296,34368,37638,41106,44784,48672,52782,57114,61680,66480,71526

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

%H R. H. Hardin, <a href="/A248462/b248462.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical for n mod 12 = 0: a(n) = n^3 + (3/2)*n^2 + 2*n.

%F Empirical for n mod 12 = 1: a(n) = n^3 + (3/2)*n^2 + 2*n + (3/2).

%F Empirical g.f.: 6*x*(1 + x^2) / ((1 - x)^4*(1 + x)). - _Colin Barker_, Nov 08 2018

%e Some solutions for n=6:

%e ..2....1....4....6....5....3....0....5....4....4....0....6....0....4....4....2

%e ..1....5....4....1....6....4....1....5....2....1....6....3....6....2....6....5

%e ..4....2....0....1....0....1....3....6....5....4....4....6....6....2....1....3

%Y Row 1 of A248461.

%K nonn

%O 1,1

%A _R. H. Hardin_, Oct 06 2014