A211459 - OEIS

%I #8 Jul 17 2018 09:00:25

%S 20,44,92,178,348,658,1260,2382,4548,8658,16604,31894,61596,119362,

%T 232212,453438,887916,1744602,3434636,6780910,13405764,26561986,

%U 52679004,104653254,208038684,414084306,824553428,1643457646,3276588012

%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 three distinct values for every i<=n and j<=n.

%H R. H. Hardin, <a href="/A211459/b211459.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) + a(n-2) - 21*a(n-3) + 16*a(n-4) + 29*a(n-5) - 34*a(n-6) - 6*a(n-7) + 12*a(n-8).

%F Empirical g.f.: 2*x*(10 - 18*x - 52*x^2 + 93*x^3 + 74*x^4 - 132*x^5 - 25*x^6 + 46*x^7) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)*(1 - 2*x^2)*(1 - 3*x^2)). - _Colin Barker_, Jul 17 2018

%e Some solutions for n=5:

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

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 12 2012