A211476 Number of -1..1 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 one or three distinct values for every i<=n and j<=n.

7, 17, 37, 79, 165, 339, 693, 1403, 2837, 5707, 11477, 23019, 46165, 92459, 185173, 370603, 741717, 1483947, 2968917, 5938859, 11879765, 23761579, 47527253, 95058603, 190125397, 380258987, 760534357, 1521085099, 3042202965, 6084438699

Offset

1,1

Links

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

Formula

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

Conjectures from Colin Barker, Jul 18 2018: (Start)

G.f.: x*(7 + 10*x - 8*x^2 - 12*x^3) / ((1 + x)*(1 - 2*x)*(1 - 2*x^2)).

a(n) = (-9*2^(n/2) + 17*2^n + 1)/3 for n even.

a(n) = (17*2^n - 3*2^((n+3)/2) - 1)/3 for n odd.

(End)

Example

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

Crossrefs

Sequence in context: A090147 A348560 A338030 * A155007 A214634 A172156

Adjacent sequences: A211473 A211474 A211475 * A211477 A211478 A211479

Keyword

nonn

Author

R. H. Hardin, Apr 12 2012

Status

approved