A211525 Number of -1..1 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 or four distinct values for every i,j,k<=n.

8, 14, 24, 44, 80, 152, 288, 560, 1088, 2144, 4224, 8384, 16640, 33152, 66048, 131840, 263168, 525824, 1050624, 2100224, 4198400, 8394752, 16785408, 33566720, 67125248, 134242304, 268468224, 536920064, 1073807360, 2147581952, 4295098368

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..79

Formula

Empirical: a(n) = 2*a(n-1) + 2*a(n-2) - 4*a(n-3).

From Colin Barker, Mar 09 2018: (Start)

G.f.: 2*x*(4 - x - 10*x^2) / ((1 - 2*x)*(1 - 2*x^2)).

a(n) = 3*2^(n/2) + 2^(n+1) for n even.

a(n) = 2^(n+1) + 2^((n+3)/2) for n odd.

(End)

Example

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

Crossrefs

Sequence in context: A275898 A248427 A090993 * A241161 A014002 A301787

Adjacent sequences: A211522 A211523 A211524 * A211526 A211527 A211528

Keyword

nonn

Author

R. H. Hardin, Apr 14 2012

Status

approved