A251421 - OEIS

%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