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%I #8 Dec 09 2018 07:27:36
%S 12,53,152,345,676,1197,1968,3057,4540,6501,9032,12233,16212,21085,
%T 26976,34017,42348,52117,63480,76601,91652,108813,128272,150225,
%U 174876,202437,233128,267177,304820,346301,391872,441793,496332,555765,620376,690457
%N Number of length 2+2 0..n arrays with the sum of medians of adjacent triples multiplied by some arrangement of +-1 equal to zero.
%H R. H. Hardin, <a href="/A253130/b253130.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/3)*n^4 + (8/3)*n^3 + (14/3)*n^2 + (10/3)*n + 1.
%F Conjectures from _Colin Barker_, Dec 09 2018: (Start)
%F G.f.: x*(3 - x)*(4 - x + 2*x^2 - x^3) / (1 - x)^5.
%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
%F (End)
%e Some solutions for n=10:
%e ..7....4....7....9....1....4....7....6....5....4....4....4....6....9....9....1
%e ..2....6...10....0....2....1...10....7....9....6...10....0....6....2....5....6
%e ..0....9....9....1....9....0....9...10....8....8....6....3....7....1....9....3
%e ..4....0....4....3....2....1....5....3....1....6....6....7....2....4....9....2
%Y Row 2 of A253129.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 27 2014
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