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%I #11 May 13 2020 18:59:53
%S 168,712,2368,8840,31176,113024,404264,1455496,5223552,18775816,
%T 67437448,242306240,870461352,3127322696,11235107264,40363689352,
%U 145010699592,520968428032,1871637364264,6724074597128,24157004951808,86786820122120
%N Number of length n+2 0..7 arrays with some pair in every consecutive three terms totalling exactly 7.
%H R. H. Hardin, <a href="/A245868/b245868.txt">Table of n, a(n) for n = 1..210</a>
%H Robert Israel, <a href="/A245868/a245868.pdf">Maple-assisted derivation of recurrence</a>
%F Empirical: a(n) = 2*a(n-1) + 6*a(n-2) - a(n-3).
%F Empirical g.f.: 8*x*(21 + 47*x - 8*x^2) / (1 - 2*x - 6*x^2 + x^3). - _Colin Barker_, Nov 04 2018
%F Empirical recurrence verified: see link. - _Robert Israel_, May 13 2020
%e Some solutions for n=6:
%e ..4....6....7....0....7....3....6....4....0....2....6....1....6....5....0....2
%e ..2....4....6....0....2....6....3....5....7....6....0....7....6....6....7....5
%e ..3....3....1....7....0....1....4....2....6....1....1....0....1....2....6....6
%e ..5....6....4....4....5....6....0....6....1....1....6....1....1....1....0....1
%e ..2....1....3....0....2....5....7....5....0....6....7....6....6....6....7....7
%e ..4....6....4....3....4....2....2....2....7....1....0....6....7....7....2....6
%e ..5....3....3....4....3....5....5....0....5....1....7....1....0....0....5....1
%e ..2....4....2....3....2....4....6....5....2....6....0....2....2....6....3....7
%Y Column 7 of A245869.
%K nonn
%O 1,1
%A _R. H. Hardin_, Aug 04 2014
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