A253122 - OEIS

%I #9 Dec 09 2018 07:34:42

%S 4,12,16,40,64,144,256,544,1024,2112,4096,8320,16384,33024,65536,

%T 131584,262144,525312,1048576,2099200,4194304,8392704,16777216,

%U 33562624,67108864,134234112,268435456,536903680,1073741824,2147549184,4294967296

%N Number of length n+2 0..1 arrays with the sum of medians of adjacent triples multiplied by some arrangement of +-1 equal to zero.

%H R. H. Hardin, <a href="/A253122/b253122.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_, Dec 09 2018: (Start)

%F G.f.: 4*x*(1 + x - 4*x^2) / ((1 - 2*x)*(1 - 2*x^2)).

%F a(n) = 2^(n/2+1) + 2^(n+1) for n even.

%F a(n) = 2^(n+1) for n odd.

%F (End)

%e Some solutions for n=10:

%e ..1....1....0....0....0....0....0....1....0....1....0....0....0....1....1....0

%e ..1....1....1....0....1....1....1....1....1....0....0....0....1....1....0....1

%e ..0....0....1....0....1....0....1....0....1....0....0....0....1....1....0....1

%e ..1....0....0....1....0....0....1....1....1....1....1....0....0....1....0....1

%e ..0....0....0....0....0....0....1....1....0....0....0....0....0....1....0....0

%e ..1....0....1....0....1....0....1....0....1....1....1....0....0....1....0....1

%e ..0....1....1....1....0....0....0....0....0....0....1....0....0....0....0....1

%e ..0....0....0....0....0....0....1....0....0....0....0....0....1....1....1....1

%e ..1....0....0....1....0....1....1....0....1....1....1....0....0....1....0....1

%e ..0....1....0....0....0....1....1....1....1....0....0....0....0....1....0....0

%e ..1....0....0....1....1....0....0....1....0....1....1....1....0....1....0....0

%e ..0....1....1....0....0....0....1....1....0....0....1....0....0....1....0....0

%Y Column 1 of A253129.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 27 2014