A199697 Number of -1..1 arrays x(0..n-1) of n elements with zero sum and no two neighbors equal.

1, 2, 6, 8, 14, 32, 56, 100, 204, 388, 722, 1416, 2750, 5256, 10222, 19944, 38650, 75272, 147142, 287120, 561018, 1098752, 2152092, 4217620, 8276376, 16250292, 31921374, 62754072, 123440514, 242921784, 478310952, 942260548, 1856994908, 3661288036

Offset

1,2

Comments

Column 1 of A199704

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

G.f.: ((x+1)^2*sqrt((1-x)/(1-x-4*x^3))-2*x-1)/x. - Stefan Hollos, Mar 08 2017

Example

All solutions for n=5
..0...-1....1...-1....1...-1...-1....0....1...-1....0....1....1....0
.-1....1...-1....1....0....1....0...-1...-1....1....1...-1...-1....1
..1....0....0...-1...-1...-1....1....0....1....0....0....1....0...-1
.-1...-1....1....1....1....0...-1....1....0....1...-1...-1...-1....1
..1....1...-1....0...-1....1....1....0...-1...-1....0....0....1...-1

Mathematica

Rest@ CoefficientList[Series[((x + 1)^2*Sqrt[(1 - x)/(1 - x - 4*x^3)] - 2 x - 1)/x, {x, 0, 34}], x] (* Michael De Vlieger, Mar 08 2017 *)

Crossrefs

Sequence in context: A107019 A269831 A048133 * A339976 A135619 A067795

Adjacent sequences: A199694 A199695 A199696 * A199698 A199699 A199700

Keyword

nonn

Author

R. H. Hardin, Nov 09 2011

Status

approved