A211576 - OEIS

%I #7 Jul 19 2018 09:49:37

%S 16,48,124,294,680,1578,3600,8458,19460,46510,108280,262542,617264,

%T 1512270,3580596,8834026,21015224,52087762,124294096,308994090,

%U 738810308,1840241022,4405749912,10987766974,26328139088,65715472894,157549520692

%N Number of -2..2 arrays x(i) of n+1 elements i=1..n+1 with set{t,u,v in 0,1}((x[i+t]+x[j+u]+x[k+v])*(-1)^(t+u+v)) having four, five or six distinct values for every i,j,k<=n.

%H R. H. Hardin, <a href="/A211576/b211576.txt">Table of n, a(n) for n = 1..64</a>

%F Empirical: a(n) = 4*a(n-1) + 7*a(n-2) - 45*a(n-3) + 10*a(n-4) + 155*a(n-5) - 130*a(n-6) - 180*a(n-7) + 216*a(n-8) + 36*a(n-9) - 72*a(n-10).

%F Empirical g.f.: 2*x*(8 - 8*x - 90*x^2 + 91*x^3 + 318*x^4 - 290*x^5 - 421*x^6 + 286*x^7 + 186*x^8 - 60*x^9) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)*(1 - 2*x^2)*(1 - 3*x^2)*(1 - 6*x^2)). - _Colin Barker_, Jul 19 2018

%e Some solutions for n=5:

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

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 16 2012