Help With Recurrence Relation Simplification

[straight_stewie]

So I have this recurrence relation: a_n = -a_n-1 , a₀ = 5.

 

This yields the pattern:

1. a₁ = -a₀ = -5
2. a₂ = -(-a₀) = -(-5) = 5
3. a₃ = -(-(-a₀) = -(-(-5) = -5
4. a₄ = -(-(-(-a₀) = 1(-(-(-5) = 5

I can deduce the pattern then is to alternate signs. I can turn this into a piecewise function:

• a_n = -a₀ n % 2 != 0; a_n = a₀ n % 2 == 0

However, I have not been able to reduce the function any further. Is this as far as it goes or can it be reduced more?

[fizzlesticks]

It doesn't get much simpler than a or -a. But if you just want to make it a single function you could do something like 

-5 * (((n & 1) * 2) - 1)

[Nineshadow]

Yeah, that's pretty much it.

Or, alternatively, you can have something like

a_n=(-1)ⁿ*a₀

[straight_stewie]

1 hour ago, Nineshadow said:

a_n=(-1)ⁿ*a₀

That's what I was looking for. I just couldn't quite put my finger on that.