A211726 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.

48, 118, 254, 516, 1024, 2002, 3898, 7562, 14676, 28484, 55362, 107750, 210032, 410146, 802044, 1571350, 3082320, 6056992, 11914916, 23476260, 46297036, 91432582, 180706966, 357595598, 708081486, 1403597900, 2783755026, 5526116978

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..54

Formula

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).

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

Example

Some solutions for n=5:
.-1....2....2....1...-2....1....2...-1....2....0....0....3....1...-2....2....0
.-1....0....2....1....0...-1....3...-1...-2...-3....2...-3....3....0...-3....3
..1....2...-2...-1...-2...-1....2....1...-2....0...-3....3....1....1....2....0
..1....0...-2...-1....2...-1....1...-1....2...-3....2...-3....3....0....0....3
..1...-1...-2...-1....2...-1....0....1....2....3...-3...-3....1....1....2...-3
..1....0....2....1...-2...-1...-1...-1....2....0....2....3....3...-1....0...-3

Crossrefs

Sequence in context: A044616 A182679 A260759 * A232938 A362045 A194952

Adjacent sequences: A211723 A211724 A211725 * A211727 A211728 A211729

Keyword

nonn

Author

R. H. Hardin, Apr 20 2012

Status

approved