%I #12 Nov 08 2018 06:33:57
%S 32,396,2292,9080,28020,72972,167576,349392,674520,1223180,2105772,
%T 3469896,5507852,8465100,12649200,18439712,26298576,36781452,50549540,
%U 68382360,91191012,120032396,156123912,200859120,255823880,322813452
%N Number of length 1+5 0..n arrays with no disjoint triples in any consecutive six terms having the same sum.
%H R. H. Hardin, <a href="/A247996/b247996.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 + (1/2)*n^5 + (35/2)*n^4 - (5/2)*n^3 + 5*n^2 + 18*n
%F Empirical for n mod 2 = 1: a(n) = n^6 + (1/2)*n^5 + (35/2)*n^4 - (5/2)*n^3 + 5*n^2 + 18*n - (15/2).
%F Conjectures from _Colin Barker_, Nov 07 2018: (Start)
%F G.f.: 4*x*(8 + 51*x + 91*x^2 + 106*x^3 + 21*x^4 + 83*x^5) / ((1 - x)^7*(1 + x)).
%F a(n) = (2*n^6 + n^5 + 35*n^4 - 5*n^3 + 10*n^2 + 36*n) / 2 for n even.
%F a(n) = (2*n^6 + n^5 + 35*n^4 - 5*n^3 + 10*n^2 + 36*n - 15) / 2 for n odd.
%F (End)
%e Some solutions for n=6:
%e 4 3 5 2 0 5 4 4 0 1 6 1 5 4 4 2
%e 4 1 5 0 3 4 0 1 0 6 4 6 4 4 1 0
%e 2 0 3 4 5 5 3 1 5 3 5 5 1 2 2 2
%e 6 1 3 1 2 0 4 1 2 4 5 1 5 2 5 0
%e 3 2 2 5 2 2 2 1 1 0 5 5 3 5 3 2
%e 0 6 5 3 5 1 2 0 0 5 6 2 3 6 2 5
%Y Row 1 of A247995.
%K nonn
%O 1,1
%A _R. H. Hardin_, Sep 28 2014