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%I #11 Nov 05 2018 03:05:12
%S 16,103,256,549,960,1579,2368,3433,4720,6351,8256,10573,13216,16339,
%T 19840,23889,28368,33463,39040,45301,52096,59643,67776,76729,86320,
%U 96799,107968,120093,132960,146851,161536,177313,193936,211719,230400,250309
%N Number of length 3+2 0..n arrays with some pair in every consecutive three terms totalling exactly n.
%H R. H. Hardin, <a href="/A245872/b245872.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6).
%F Conjectures from _Colin Barker_, Nov 04 2018: (Start)
%F G.f.: x*(16 + 71*x + 34*x^2 - 2*x^3 + 2*x^4 - x^5) / ((1 - x)^4*(1 + x)^2).
%F a(n) = 1 + 5*n + 13*n^2 + 5*n^3 for n even.
%F a(n) = -5 + 3*n + 13*n^2 + 5*n^3 for n odd.
%F (End)
%e Some solutions for n=10:
%e 7 7 7 5 1 9 3 6 4 9 10 10 5 2 9 0
%e 3 4 3 5 1 9 10 4 2 1 8 0 7 4 5 6
%e 5 6 5 4 9 1 7 10 8 4 2 10 5 6 5 4
%e 5 2 7 5 5 4 3 0 8 6 4 0 5 4 5 5
%e 4 4 3 6 5 9 10 6 2 4 6 6 8 1 3 6
%Y Row 3 of A245869.
%K nonn
%O 1,1
%A _R. H. Hardin_, Aug 04 2014
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