So annoying to get an integer answer without an explanation!

However, there is a similar problem, with x³ - x - 1 = 0, leading to a well-known sequence.

Now for x³ - x - 1 = 0, the roots are: x~~1.3247,x~~-0.66236-0.56228i, x~~-0.66236+0.56228i,

while for x³ - x + 1 = 0, the roots are:
x~~-1.3247, x~~0.66236-0.56228i, x~~0.66236+0.56228i, so there's just a sign change in the real part.

Since we are raising to an even power, the result is the same for either equation, see:

http://mathworld.wolfram.com/PerrinSequence.html

http://en.wikipedia.org/wiki/Perrin_number