Here's a nifty wee egg chart I found recently which may help to answer your question!
The more learned members may want to check me on this next but my assessment of your question is as follows:
Pairing Number One
EE rooster = Blue / ?? Egg genes
(Blue from americauna parent & ?? from non americaunana parent)
Ameraucana Hen = Blue / Blue Egg genes
A pairing of these two will give you 50% chicks with Blue/Blue eggs and 50% chicks with Blue/?? eggs.
You will be able to make an intelligent guess what the ?? gene was as soon as your pullets start laying.
If they are laying "green/olive" eggs then I would say that your EE rooster had Blue / Brown egg genes.
Subsequent Pairings
EE rooster = Blue / Brown egg genes (Assumed based on above)
F1 Hen From Above (Laying Green/Olive Eggs) = Blue / Brown egg genes
A pairing of these birds would potentially give you:
Blue Eggs (if Blue/Blue passes down)
Brown Eggs (if Brown/Brown passes down)
Varying shades of Green/Olive (If Blue/Brown passes down)
Describing Birds
In my mind an "Easter Egger" is any bird that has one parent that was Araucana or Americauna (depending what you call it where you are) - regardless of what colour egg it lays.
An "Olive Egger" simply describes the colour of the egg it's laying?
In my mind technically you could have a bird that is described as both a EE and OE?
Your Eggs
To be honest, in the picture you posted, I see your colours falling more to the brown end of the colour scale than the blue end
Ultimately easter eggers are just mutts that happen to carry the blue egg gene. That doesn't mean they don't have value and they certainly are pretty and can lay beautiful eggs.
What you would get from the above matings would heavily lean toward olive eggs. If you want blue eggs, breed a blue egg layer to another blue egg layer. Remember that to lay a blue egg means the chicken has a combination of a gene for white eggs and the oocyanin blue egg gene. Olive layers have genes to produce porphyrin which means the white egg gene is either missing or suppressed. It is time consuming to breed out the porphryin genes. Ask me how I know this.
Ultimately easter eggers are just mutts that happen to carry the blue egg gene. That doesn't mean they don't have value and they certainly are pretty and can lay beautiful eggs.
What you would get from the above matings would heavily lean toward olive eggs. If you want blue eggs, breed a blue egg layer to another blue egg layer. Remember that to lay a blue egg means the chicken has a combination of a gene for white eggs and the oocyanin blue egg gene. Olive layers have genes to produce porphyrin which means the white egg gene is either missing or suppressed. It is time consuming to breed out the porphryin genes. Ask me how I know this.
I now have my desired Olive eggers in my flock that I hatched from a local breeder. I also just successfully hatched shipped eggs; 7 Crested Cream Legbar and 7 Silverudd’s blue. I’m just trying to figure out the correct way to advertise hatching eggs from my current layers! I think I’m safe with labeling them as a mix of both Easter Eggers and Olive Eggers but I was asked if they are F1 or F2 Olive eggers and that’s what I’m not too certain on!
BTW I don’t have a good camera to get good pictures with. My eggs are much more mint green (lighter ones) and Olive green than the brown hues showing in the photo. One did start off really grey when that hen first started laying but it’s became more Olive now.
I think I’m safe with labeling them as a mix of both Easter Eggers and Olive Eggers but I was asked if they are F1 or F2 Olive eggers and that’s what I’m not too certain on!
I'm assuming that the reason a person might ask if a hen is F1 or F2 Olive Egger is so they can try and work out what eggs they might get if breeding from that hen.
If it were me I'd avoid saying F1 or F2 and simply advise the known parentage, pls show examples of their eggs, and let them decide for themselves
If you gave them the basic info you gave us above, surely that would satisfy their curiosity??
Once you get a couple generations in what they're called honestly just depends what color eggs they lay. Any blue/green=EE, any dark green is OE. You could get some brown or even white eggers, too. I'd just call them all EEs.
I had birds two years ago that would have babies that could lay white, brown, or any shade of blue/green eggs due to all the parents being heterozygous for blue/white and brown/non-brown. Called them rainbow eggers. Just brown and green eggs in my flock now though, genetic drift man.