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%I #9 Mar 20 2018 06:51:59
%S 2,12,12,40,56,144,240,544,992,2112,4032,8320,16256,33024,65280,
%T 131584,261632,525312,1047552,2099200,4192256,8392704,16773120,
%U 33562624,67100672,134234112,268419072,536903680,1073709056,2147549184,4294901760
%N Number of length n+2 0..1 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.
%C Column 1 of A251428.
%H R. H. Hardin, <a href="/A251421/b251421.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-1) +2*a(n-2) -4*a(n-3).
%F Conjectures from _Colin Barker_, Mar 20 2018: (Start)
%F G.f.: 2*x*(1 + 4*x - 8*x^2) / ((1 - 2*x)*(1 - 2*x^2)).
%F a(n) = 2*(2^(n/2) + 2^n) for n even.
%F a(n) = 2*(2^n - 2^((n-3)/2+1)) for n odd.
%F (End)
%e Some solutions for n=10:
%e ..1....0....1....1....0....0....0....1....1....0....1....1....1....0....1....0
%e ..0....1....1....0....1....1....1....0....0....1....0....1....1....1....0....0
%e ..0....1....1....0....1....0....0....0....1....0....0....1....1....0....0....1
%e ..0....1....0....0....1....0....0....1....0....1....1....1....1....0....1....1
%e ..1....1....1....1....1....0....1....0....0....0....0....0....0....1....0....0
%e ..1....1....0....1....1....0....1....0....1....0....1....1....0....0....0....1
%e ..0....1....0....0....0....0....0....1....0....1....0....0....1....0....0....0
%e ..1....1....0....0....0....1....0....1....0....0....1....0....1....1....0....1
%e ..1....1....0....1....0....0....0....0....1....1....0....0....0....1....0....1
%e ..1....1....0....0....0....0....0....0....0....0....0....0....1....0....0....0
%e ..0....1....1....0....0....0....1....1....1....1....1....0....1....1....1....1
%e ..0....0....1....0....1....1....0....0....1....1....0....0....0....1....0....0
%Y Cf. A251428.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 02 2014
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