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%I #8 Nov 05 2018 18:09:28
%S 88,1501,7744,31465,82968,199141,397504,754321,1292440,2144941,
%T 3335808,5074681,7380184,10560565,14620288,19990561,26650584,35181181,
%U 45522880,58435081,73803928,92598661,114633024,141119665,171779608,208104781
%N Number of length 4+3 0..n arrays with some pair in every consecutive four terms totalling exactly n.
%H R. H. Hardin, <a href="/A245954/b245954.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*(88 + 1325*x + 4478*x^2 + 12178*x^3 + 8990*x^4 + 2708*x^5 - 310*x^6 - 658*x^7 + 2*x^8 - x^9) / ((1 - x)^6*(1 + x)^4).
%F a(n) = 1 + 34*n + 6*n^2 - 16*n^3 + 66*n^4 + 15*n^5 for n even.
%F a(n) = 58 + 57*n - 80*n^2 - 28*n^3 + 66*n^4 + 15*n^5 for n odd.
%F (End)
%e Some solutions for n=6:
%e ..0....0....0....0....0....1....1....4....4....1....1....4....4....3....0....3
%e ..6....6....5....5....5....4....3....1....6....0....0....5....3....6....0....2
%e ..6....5....2....1....6....2....1....5....5....6....6....1....0....5....2....4
%e ..3....1....4....4....0....2....5....5....0....0....0....5....6....1....4....1
%e ..3....0....5....2....0....1....5....6....6....0....6....3....5....5....3....4
%e ..6....1....1....1....3....4....6....0....5....5....4....6....1....5....2....2
%e ..2....5....2....5....6....4....0....1....2....1....0....0....2....5....3....0
%Y Row 4 of A245950
%K nonn
%O 1,1
%A _R. H. Hardin_, Aug 08 2014
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