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%I #8 Nov 04 2018 08:02:19
%S 10,45,100,193,318,493,712,993,1330,1741,2220,2785,3430,4173,5008,
%T 5953,7002,8173,9460,10881,12430,14125,15960,17953,20098,22413,24892,
%U 27553,30390,33421,36640,40065,43690,47533,51588,55873,60382,65133,70120,75361
%N Number of length 2+2 0..n arrays with some pair in every consecutive three terms totalling exactly n.
%H R. H. Hardin, <a href="/A245871/b245871.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 Conjectures from _Colin Barker_, Nov 04 2018: (Start)
%F G.f.: x*(10 + 15*x - 15*x^2 + 3*x^3 - x^4) / ((1 - x)^4*(1 + x)).
%F a(n) = 1 + 4*n + 7*n^2 + n^3 for n even.
%F a(n) = -2 + 4*n + 7*n^2 + n^3 for n odd.
%F (End)
%e Some solutions for n=10:
%e ..9....1....8....0....9....0...10....4....3....5....8....4....3...10....3....9
%e ..0....9....4....6....0...10....0....4....4....5....2....4....4....2....1....5
%e .10....1....6....4...10....0...10....6....6....9...10....6....6....8....9....1
%e .10....0....0....0....1....3....4....3....0....1....8....1....6....8....7....5
%Y Row 2 of A245869.
%K nonn
%O 1,1
%A _R. H. Hardin_, Aug 04 2014
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