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%I #7 Dec 01 2018 15:20:49
%S 12,83,264,687,1428,2729,4680,7661,11764,17535,25056,35067,47628,
%T 63701,83312,107673,136764,172075,213528,262919,320100,387201,463992,
%U 552965,653796,769367,899248,1046739,1211292,1396653,1602144,1831985,2085356
%N Number of length 3+2 0..n arrays with the sum of the maximum minus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.
%H R. H. Hardin, <a href="/A252179/b252179.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 3*a(n-1) - 8*a(n-3) + 6*a(n-4) + 6*a(n-5) - 8*a(n-6) + 3*a(n-8) - a(n-9).
%F Empirical for n mod 2 = 0: a(n) = (1/60)*n^5 + (17/16)*n^4 + (14/3)*n^3 + (11/2)*n^2 + (77/30)*n + 1.
%F Empirical for n mod 2 = 1: a(n) = (1/60)*n^5 + (17/16)*n^4 + (14/3)*n^3 + (39/8)*n^2 + (79/60)*n + (1/16).
%F Empirical g.f.: x*(12 + 47*x + 15*x^2 - 9*x^3 - 41*x^4 - 13*x^5 + 3*x^6 + 3*x^7 - x^8) / ((1 - x)^6*(1 + x)^3). - _Colin Barker_, Dec 01 2018
%e Some solutions for n=6:
%e ..6....6....2....5....5....6....0....2....5....0....0....4....4....4....0....2
%e ..0....0....0....5....5....1....3....1....3....1....1....4....5....0....3....1
%e ..4....0....3....3....5....2....3....1....6....1....1....6....6....1....2....5
%e ..4....2....0....0....0....0....4....5....6....1....2....6....3....2....2....6
%e ..2....4....6....3....3....3....0....0....0....0....3....2....1....3....4....5
%Y Row 3 of A252177.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 15 2014
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