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%I #7 Nov 08 2018 06:34:11
%S 32,333,1804,6545,18636,44677,94568,182049,325480,548381,880212,
%T 1356913,2021684,2925525,4128016,5697857,7713648,10264429,13450460,
%U 17383761,22188892,28003493,34979064,43281505,53091896,64607037,78040228,93621809
%N Number of length 1+5 0..n arrays with some disjoint triples in each consecutive six terms having the same sum.
%H R. H. Hardin, <a href="/A248069/b248069.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 5*a(n-1) - 9*a(n-2) + 5*a(n-3) + 5*a(n-4) - 9*a(n-5) + 5*a(n-6) - a(n-7).
%F Empirical for n mod 2 = 0: a(n) = (11/2)*n^5 - (5/2)*n^4 + (45/2)*n^3 + 10*n^2 - 12*n + 1.
%F Empirical for n mod 2 = 1: a(n) = (11/2)*n^5 - (5/2)*n^4 + (45/2)*n^3 + 10*n^2 - 12*n + (17/2).
%F Empirical g.f.: x*(32 + 173*x + 427*x^2 + 362*x^3 + 322*x^4 + 5*x^5 - x^6) / ((1 - x)^6*(1 + x)). - _Colin Barker_, Nov 08 2018
%e Some solutions for n=6:
%e ..6....5....0....5....0....2....6....1....2....3....5....4....1....5....2....2
%e ..1....1....4....6....1....6....6....5....1....2....3....2....6....6....3....1
%e ..4....0....3....4....0....3....3....5....2....1....0....4....5....3....6....1
%e ..6....5....2....5....5....0....3....1....5....6....1....6....2....2....5....6
%e ..3....1....3....4....3....4....1....4....4....2....2....5....6....2....4....5
%e ..6....0....4....6....1....3....1....4....2....4....5....1....6....0....0....3
%Y Row 1 of A248068.
%K nonn
%O 1,1
%A _R. H. Hardin_, Sep 30 2014
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