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A245952 Number of length 2+3 0..n arrays with some pair in every consecutive four terms totalling exactly n.

%I A245952 #8 Nov 05 2018 11:36:15
%S A245952 26,197,676,1889,3966,7669,13064,21281,32290,47621,67116,92737,124166,
%T A245952 163829,211216,269249,337194,418501,512180,622241,747406,892277,
%U A245952 1055256,1241569,1449266,1684229,1944124,2235521,2555670,2911861,3300896,3730817
%N A245952 Number of length 2+3 0..n arrays with some pair in every consecutive four terms totalling exactly n.
%H A245952 R. H. Hardin, <a href="/A245952/b245952.txt">Table of n, a(n) for n = 1..210</a>
%F A245952 Empirical: a(n) = 2*a(n-1) + 2*a(n-2) - 6*a(n-3) + 6*a(n-5) - 2*a(n-6) - 2*a(n-7) + a(n-8).
%F A245952 Conjectures from _Colin Barker_, Nov 05 2018: (Start)
%F A245952 G.f.: x*(26 + 145*x + 230*x^2 + 299*x^3 + 18*x^4 - 141*x^5 - 2*x^6 + x^7) / ((1 - x)^5*(1 + x)^3).
%F A245952 a(n) = 1 + 12*n - 5*n^2 + 18*n^3 + 3*n^4 for n even.
%F A245952 a(n) = 16 - 5*n - 6*n^2 + 18*n^3 + 3*n^4 for n odd.
%F A245952 (End)
%e A245952 Some solutions for n=10:
%e A245952 ..3....1....2....0....6....0....7....8....4...10....2....9....9....3....0....3
%e A245952 ..9....1....2....3....6....8....0....5....9....5....6....3....2....0....1....2
%e A245952 ..1....9...10...10....2....2...10....5....1....6....1....7....0...10....9....8
%e A245952 ..1....6....0....0....4....0....9....0....6....5....4....2....8....6....8...10
%e A245952 ..1....8...10....2...10....9....6....6....1....5....7....4....1....3...10....2
%Y A245952 Row 2 of A245950.
%K A245952 nonn
%O A245952 1,1
%A A245952 _R. H. Hardin_, Aug 08 2014