A211465 - OEIS

A211465

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

%I #7 Jul 18 2018 05:25:22

%S 24,116,556,2652,12588,59484,279932,1312364,6131052,28550492,

%T 132555868,613748556,2834515596,13060107900,60044009084,275496757868,

%U 1261682707500,5768039837468,26327131807900,119984300243340,546053643671244

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

%H R. H. Hardin, <a href="/A211465/b211465.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 12*a(n-1) - 45*a(n-2) + 40*a(n-3) + 46*a(n-4) + 8*a(n-5).

%F Empirical g.f.: 4*x*(6 - 43*x + 61*x^2 + 60*x^3 + 10*x^4) / ((1 - 4*x)*(1 - 4*x - x^2)*(1 - 4*x - 2*x^2)). - _Colin Barker_, Jul 18 2018

%e Some solutions for n=5.

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

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 12 2012