A211459 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 three distinct values for every i<=n and j<=n.

20, 44, 92, 178, 348, 658, 1260, 2382, 4548, 8658, 16604, 31894, 61596, 119362, 232212, 453438, 887916, 1744602, 3434636, 6780910, 13405764, 26561986, 52679004, 104653254, 208038684, 414084306, 824553428, 1643457646, 3276588012

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 4*a(n-1) + a(n-2) - 21*a(n-3) + 16*a(n-4) + 29*a(n-5) - 34*a(n-6) - 6*a(n-7) + 12*a(n-8).

Empirical g.f.: 2*x*(10 - 18*x - 52*x^2 + 93*x^3 + 74*x^4 - 132*x^5 - 25*x^6 + 46*x^7) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)*(1 - 2*x^2)*(1 - 3*x^2)). - Colin Barker, Jul 17 2018

Example

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

Crossrefs

Sequence in context: A039322 A043145 A043925 * A256870 A134619 A219716

Adjacent sequences: A211456 A211457 A211458 * A211460 A211461 A211462

Keyword

nonn

Author

R. H. Hardin, Apr 12 2012

Status

approved