A211687 - OEIS

%I #8 Jul 19 2018 14:07:45

%S 68,156,318,604,1144,2108,3924,7236,13486,25108,47168,88856,168588,

%T 321220,615390,1184204,2288040,4438780,8636484,16862164,32990542,

%U 64729172,127184496,250474872,493763644,975154132,1927138430,3814135532

%N Number of -4..4 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="/A211687/b211687.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) + 6*a(n-2) - 41*a(n-3) + 6*a(n-4) + 154*a(n-5) - 109*a(n-6) - 256*a(n-7) + 262*a(n-8) + 175*a(n-9) - 230*a(n-10) - 30*a(n-11) + 60*a(n-12).

%F Empirical g.f.: 2*x*(34 - 58*x - 357*x^2 + 592*x^3 + 1404*x^4 - 2231*x^5 - 2564*x^6 + 3806*x^7 + 2164*x^8 - 2860*x^9 - 668*x^10 + 704*x^11) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)*(1 - 2*x^2)*(1 - 3*x^2)*(1 - 5*x^2 + 5*x^4)). - _Colin Barker_, Jul 19 2018

%e Some solutions for n=5:

%e ..2....1....0....0...-2....3...-4...-2...-2...-3...-1....1....0...-1....0....3

%e ..0....2....2...-4....3....4....4....0...-1...-1....2....3...-2....1....4...-3

%e ..2....1....0....2....1....3...-4....1....0....1....0....1....0....0...-4....0

%e ..0....2...-2...-4....3....2....4....2....2...-1...-4...-2....2....1....0....3

%e .-4...-4....2....0...-2....3...-4....1....0....1....0....1...-2...-1....4....0

%e ..4....2....0...-4....3....2....0....0...-1....3....2....3....2....0....0....3

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 18 2012