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Not quite. A RIR rooster over a Barred Rock gives you a black sex link. The pullet offspring would be solid black (probably with red leakage around the neck) while the male offspring would be black barred. If you want a red sex link, you need to cross a rooster with the gold gene with a hen with a silver gene. A RIR rooster over a Delaware hen or maybe a White Rock hen gives you a red sex link. In these, the pullet is red usually with a black tail (and probably some black around the neck) while the rooster is basically white with a black tail and black around the neck, but also some rust-color around the saddle and hackles. Or if dominant white is involved, the tails or whatever can be white instead of black. Lots of possibilities.
As others mentioned a Barred Rock rooster over a RIR hen will give you both male and female chicks that look a whole lot like the Barred Rock. There may be some red leakage in the adult plumage, but they will mostly be black and white barred. If you cross the offspring of this cross, you can get a variety of colors and patterns. According to Henks calculator, here are some of the colors and patterns the male offspring of the crosses could be.
black patterned salmon barred
black patterned yellow/golden columbian barred
black patterned yellow/golden wheaten barred
black patterned redshouldered/cream columbian barred
black patterned silver columbian barred
black patterned silver wheaten barred
black unicolor barred
Then here is part of the list of what the pullets could look like.
black patterned salmon barred
black patterned salmon
black patterned gold columbian barred
black patterned gold columbian
black patterned gold wheaten barred
black patterned gold wheaten
black patterned red columbian barred
black patterned red columbian
black patterned red wheaten barred
black patterned red wheaten
black patterned silver columbian barred
black patterned silver columbian
black patterned silver wheaten barred
black patterned silver wheaten
black unicolor barred
black unicolor
Neither of these lists is complete and Im not going to pretend I could recognize all these different colors and patterns if I saw them. To me it is part of the fun of crossing mutts. You never know what you will get.
Tuesdays Chicks, it is not so much that hereditary traits skip a generation. It is more that recessive genes can pair up when you cross crosses. There are a lot more than two or three genes involved in colors and patterns. Not all are either dominant or recessive. Sometimes certain genes can partially express themselves, so if two combine neither may dominate but both may have some effect.