|
%I #8 Jul 20 2018 06:02:40
%S 48,118,254,516,1024,2002,3898,7562,14676,28484,55362,107750,210032,
%T 410146,802044,1571350,3082320,6056992,11914916,23476260,46297036,
%U 91432582,180706966,357595598,708081486,1403597900,2783755026,5526116978
%N Number of -3..3 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 two, three, four or five distinct values for every i,j,k<=n.
%H R. H. Hardin, <a href="/A211726/b211726.txt">Table of n, a(n) for n = 1..54</a>
%F Empirical: a(n) = 5*a(n-1) - 36*a(n-3) + 41*a(n-4) + 82*a(n-5) - 151*a(n-6) - 54*a(n-7) + 204*a(n-8) - 28*a(n-9) - 110*a(n-10) + 36*a(n-11) + 20*a(n-12) - 8*a(n-13).
%F Empirical g.f.: 2*x*(24 - 61*x - 168*x^2 + 487*x^3 + 362*x^4 - 1374*x^5 - 189*x^6 + 1681*x^7 - 212*x^8 - 857*x^9 + 224*x^10 + 148*x^11 - 52*x^12) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)*(1 - 2*x^2)*(1 - x - 2*x^2 + x^3)*(1 - 4*x^2 + 2*x^4)). - _Colin Barker_, Jul 20 2018
%e Some solutions for n=5:
%e .-1....2....2....1...-2....1....2...-1....2....0....0....3....1...-2....2....0
%e .-1....0....2....1....0...-1....3...-1...-2...-3....2...-3....3....0...-3....3
%e ..1....2...-2...-1...-2...-1....2....1...-2....0...-3....3....1....1....2....0
%e ..1....0...-2...-1....2...-1....1...-1....2...-3....2...-3....3....0....0....3
%e ..1...-1...-2...-1....2...-1....0....1....2....3...-3...-3....1....1....2...-3
%e ..1....0....2....1...-2...-1...-1...-1....2....0....2....3....3...-1....0...-3
%K nonn
%O 1,1
%A _R. H. Hardin_, Apr 20 2012
| 