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%I #8 Nov 29 2018 10:37:40
%S 12,41,116,237,432,725,1128,1641,2316,3145,4148,5357,6776,8413,10328,
%T 12489,14924,17689,20764,24149,27928,32061,36568,41513,46868,52641,
%U 58924,65653,72856,80621,88896,97681,107092,117057,127596,138805,150624,163061
%N Number of length 2+2 0..n arrays with the sum of the maximum minus twice the median plus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.
%H R. H. Hardin, <a href="/A251429/b251429.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = a(n-1) + 2*a(n-3) - a(n-4) - a(n-5) - a(n-6) - a(n-7) + 2*a(n-8) + a(n-10) - a(n-11).
%F Empirical for n mod 12 = 0: a(n) = (79/27)*n^3 + (29/18)*n^2 + (17/3)*n + 1
%F Empirical for n mod 12 = 1: a(n) = (79/27)*n^3 + (29/18)*n^2 + (17/3)*n + (97/54)
%F Empirical for n mod 12 = 2: a(n) = (79/27)*n^3 + (29/18)*n^2 + (43/9)*n + (43/27)
%F Empirical for n mod 12 = 3: a(n) = (79/27)*n^3 + (29/18)*n^2 + (17/3)*n + (11/2)
%F Empirical for n mod 12 = 4: a(n) = (79/27)*n^3 + (29/18)*n^2 + (17/3)*n + (35/27)
%F Empirical for n mod 12 = 5: a(n) = (79/27)*n^3 + (29/18)*n^2 + (43/9)*n + (113/54)
%F Empirical for n mod 12 = 6: a(n) = (79/27)*n^3 + (29/18)*n^2 + (17/3)*n + 1
%F Empirical for n mod 12 = 7: a(n) = (79/27)*n^3 + (29/18)*n^2 + (17/3)*n + (313/54)
%F Empirical for n mod 12 = 8: a(n) = (79/27)*n^3 + (29/18)*n^2 + (43/9)*n + (43/27)
%F Empirical for n mod 12 = 9: a(n) = (79/27)*n^3 + (29/18)*n^2 + (17/3)*n + (3/2)
%F Empirical for n mod 12 = 10: a(n) = (79/27)*n^3 + (29/18)*n^2 + (17/3)*n + (35/27)
%F Empirical for n mod 12 = 11: a(n) = (79/27)*n^3 + (29/18)*n^2 + (43/9)*n + (329/54)
%F Empirical g.f.: x*(12 + 29*x + 75*x^2 + 97*x^3 + 125*x^4 + 114*x^5 + 98*x^6 + 55*x^7 + 27*x^8 + x^9 - x^10) / ((1 - x)^4*(1 + x)*(1 + x^2)*(1 + x + x^2)^2). - _Colin Barker_, Nov 29 2018
%e Some solutions for n=10:
%e ..1....1....5....1....6....1....1....0....5....4....8....2....7....8....0....6
%e ..7....8...10....7....4....6....3....3....6....6....3....6....2....6....6....7
%e .10....3....7....3....3...10....5....1....3....7....9....5...10....6....2....1
%e ..7....7....8....9....6....1....1....4....5....4....1....9....7....8....5....9
%Y Row 2 of A251428.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 02 2014