%I #8 Jul 17 2018 15:39:13

%S 24,56,128,254,516,982,1904,3578,6812,12786,24224,45658,86660,164422,

%T 313660,599546,1150980,2216138,4281996,8299742,16133004,31452126,

%U 61458520,120403946,236321944,464854866,915752544,1807260018,3570943416

%N Number of -2..2 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 two or three distinct values for every i<=n and j<=n.

%H R. H. Hardin, <a href="/A211461/b211461.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) + 3*a(n-2) - 28*a(n-3) + 11*a(n-4) + 67*a(n-5) - 49*a(n-6) - 63*a(n-7) + 52*a(n-8) + 18*a(n-9) - 12*a(n-10).

%F Empirical g.f.: 2*x*(12 - 20*x - 84*x^2 + 123*x^3 + 210*x^4 - 242*x^5 - 222*x^6 + 175*x^7 + 71*x^8 - 46*x^9) / ((1 - 2*x)*(1 - x - x^2)*(1 - 2*x^2)*(1 - 3*x^2)*(1 - x - 2*x^2 + x^3)). - _Colin Barker_, Jul 17 2018

%e Some solutions for n=5:

%e ..2....1....2...-2...-2...-2...-1...-2....2...-1...-1....1....0....0....0....1

%e ..0...-1....1....0....0....1....0...-1....2....0....1....0....2...-1...-1...-1

%e .-2....0....0...-2....1...-2....1....0...-2...-1...-1...-1...-2....0....0....0

%e ..0....2....1....0...-1....0...-1....1....2....0....1....1....2....1...-1....1

%e ..2....0....0....1....1...-2....0....0....2....2....0...-1....0...-1....0...-1

%e ..0....2....1....0...-1....0...-1...-1....2...-2...-1....1....2....1....2....1

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 12 2012