A211479 - OEIS

%I #7 Jul 18 2018 07:47:27

%S 8,22,58,150,382,962,2402,5958,14702,36130,88498,216198,527038,

%T 1282562,3116738,7565190,18345422,44452642,107643922,260526918,

%U 630270622,1524213890,3684989858,8906776518,21523708718,52004525602,125633423218

%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 two, three or four distinct values for every i<=n and j<=n.

%H R. H. Hardin, <a href="/A211479/b211479.txt">Table of n, a(n) for n = 1..210</a>

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

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

%F G.f.: 2*x*(4 - 5*x - 3*x^2) / ((1 - 2*x)*(1 - 2*x - x^2)).

%F a(n) = -3*2^n + (3-2*sqrt(2))*(1-sqrt(2))^n + (1+sqrt(2))^n*(3+2*sqrt(2)).

%F (End)

%e Some solutions for n=5:

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

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 12 2012