Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #7 Nov 04 2018 13:05:08
%S 42,553,1764,4753,9726,18505,31176,50401,76050,111721,156972,216433,
%T 289254,381193,490896,625345,782586,970921,1187700,1442641,1732302,
%U 2067913,2445144,2876833,3357666,3902185,4503996,5179441,5920950,6746761
%N Number of length 5+2 0..n arrays with some pair in every consecutive three terms totalling exactly n.
%H R. H. Hardin, <a href="/A245874/b245874.txt">Table of n, a(n) for n = 1..210</a>
%F 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 Conjectures from _Colin Barker_, Nov 04 2018: (Start)
%F G.f.: x*(42 + 469*x + 574*x^2 + 371*x^3 + 10*x^4 - 121*x^5 - 2*x^6 + x^7) / ((1 - x)^5*(1 + x)^3).
%F a(n) = 1 + 12*n + 26*n^2 + 39*n^3 + 7*n^4 for n even.
%F a(n) = -9 - 18*n + 23*n^2 + 39*n^3 + 7*n^4 for n odd.
%F (End)
%e Some solutions for n=10:
%e ..9....4...10....8....2....8....7....8....7....7....6....9....3....2....5....0
%e ..0....6....0....2....6....4....1....4....0....4....4....7....7....1....5....4
%e .10....6...10....3....4....6....9....2...10....6....6....3....3....9....5...10
%e ..0....4....7....7....6....1....3....8....3....8....4....7....4...10....6....0
%e ..5....0....3....8....4....9....7...10....7....2...10....5....7....1....4....4
%e .10...10....9....2....6....1....7....0...10....8....0....5....3....9....6....6
%e ..0....5....1....6....7....3....3....9....0....8....8....2....2....2....8....8
%Y Row 5 of A245869.
%K nonn
%O 1,1
%A _R. H. Hardin_, Aug 04 2014