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%I #8 Nov 08 2018 19:33:45
%S 42,546,3372,13500,41670,107502,243576,499992,949890,1695450,2874852,
%T 4669716,7313502,11100390,16395120,23643312,33382746,46255122,
%U 63018780,84561900,111916662,146273886,188998632,241646280,305979570,383986122
%N Number of length 1+5 0..n arrays with no three disjoint pairs in any consecutive six terms having the same sum.
%H R. H. Hardin, <a href="/A248449/b248449.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 6*a(n-1) - 14*a(n-2) + 14*a(n-3) - 14*a(n-5) + 14*a(n-6) - 6*a(n-7) + a(n-8).
%F Empirical for n mod 2 = 0: a(n) = n^6 + 6*n^5 + (15/2)*n^4 + 20*n^3 + 5*n^2 - 5*n.
%F Empirical for n mod 2 = 1: a(n) = n^6 + 6*n^5 + (15/2)*n^4 + 20*n^3 + 5*n^2 - 5*n + (15/2).
%F Empirical g.f.: 6*x*(7 + 49*x + 114*x^2 + 54*x^3 + 39*x^4 - 23*x^5) / ((1 - x)^7*(1 + x)). - _Colin Barker_, Nov 08 2018
%e Some solutions for n=6:
%e ..2....3....1....3....4....3....1....1....4....0....2....1....0....0....1....0
%e ..5....1....3....4....2....3....5....1....0....2....2....2....6....0....0....3
%e ..4....0....5....2....2....1....3....3....3....3....0....5....5....1....5....3
%e ..4....2....3....3....3....5....2....2....2....2....4....5....3....3....4....0
%e ..0....2....2....4....2....2....6....0....4....3....3....4....2....1....3....3
%e ..4....0....2....3....2....3....5....5....3....1....6....0....6....6....1....2
%Y Row 1 of A248448.
%K nonn
%O 1,1
%A _R. H. Hardin_, Oct 06 2014