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A211476 Number of -1..1 arrays x(i) of n+1 elements i=1..n+1 with x(i)+x(j), x(i+1)+x(j+1), -(x(i)+x(j+1)), and -(x(i+1)+x(j)) having one or three distinct values for every i<=n and j<=n. 1

%I #8 Jul 18 2018 05:31:11

%S 7,17,37,79,165,339,693,1403,2837,5707,11477,23019,46165,92459,185173,

%T 370603,741717,1483947,2968917,5938859,11879765,23761579,47527253,

%U 95058603,190125397,380258987,760534357,1521085099,3042202965,6084438699

%N Number of -1..1 arrays x(i) of n+1 elements i=1..n+1 with x(i)+x(j), x(i+1)+x(j+1), -(x(i)+x(j+1)), and -(x(i+1)+x(j)) having one or three distinct values for every i<=n and j<=n.

%H R. H. Hardin, <a href="/A211476/b211476.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) + 4*a(n-2) - 2*a(n-3) - 4*a(n-4).

%F Conjectures from _Colin Barker_, Jul 18 2018: (Start)

%F G.f.: x*(7 + 10*x - 8*x^2 - 12*x^3) / ((1 + x)*(1 - 2*x)*(1 - 2*x^2)).

%F a(n) = (-9*2^(n/2) + 17*2^n + 1)/3 for n even.

%F a(n) = (17*2^n - 3*2^((n+3)/2) - 1)/3 for n odd.

%F (End)

%e Some solutions for n=5:

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

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 12 2012

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