cp's OEIS Frontend

A251421 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.

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