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%I #9 Nov 05 2018 06:34:23
%S 110,2967,12100,40901,97602,214315,404264,727017,1200310,1920671,
%T 2909100,4309357,6143690,8614131,11741392,15797585,20798334,27098407,
%U 34704020,44065941,55175890,68594747,84293880,102959161,124534982,149847855
%N Number of length 7+2 0..n arrays with some pair in every consecutive three terms totalling exactly n.
%H R. H. Hardin, <a href="/A245876/b245876.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-1) + 3*a(n-2) - 8*a(n-3) - 2*a(n-4) + 12*a(n-5) - 2*a(n-6) - 8*a(n-7) + 3*a(n-8) + 2*a(n-9) - a(n-10).
%F Conjectures from _Colin Barker_, Nov 05 2018: (Start)
%F G.f.: x*(110 + 2747*x + 5836*x^2 + 8680*x^3 + 3456*x^4 - 2178*x^5 - 1148*x^6 - 224*x^7 + 2*x^8 - x^9) / ((1 - x)^6*(1 + x)^4).
%F a(n) = 1 + 37*n + 43*n^2 + 126*n^3 + 89*n^4 + 9*n^5 for n even.
%F a(n) = 7 - 76*n - 41*n^2 + 122*n^3 + 89*n^4 + 9*n^5 for n odd.
%F (End)
%e Some solutions for n=5:
%e ..2....4....0....4....0....0....2....3....4....2....3....3....4....1....1....5
%e ..2....1....5....3....2....3....4....0....1....0....3....5....3....3....0....0
%e ..3....2....1....2....3....2....1....5....5....5....2....0....2....2....4....5
%e ..2....3....4....3....0....5....3....0....0....3....3....1....5....5....5....2
%e ..3....3....1....2....5....3....4....0....4....2....0....4....3....3....0....3
%e ..3....2....2....4....3....2....1....5....1....0....5....2....2....2....5....5
%e ..2....2....3....1....2....2....4....3....4....3....2....1....2....3....4....2
%e ..3....3....2....0....1....3....2....2....2....2....0....3....3....2....1....0
%e ..1....2....4....4....3....2....1....0....3....4....3....2....5....4....5....5
%Y Row 7 of A245869.
%K nonn
%O 1,1
%A _R. H. Hardin_, Aug 04 2014
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