Another solution requiring also a bit of programming is:
l<-letters[1:3]
c2<-c()
for(i in 1:3){c2<-c(c2,paste(letters[i],letters[i:3],sep=""))}
c2
[1] "aa" "ab" "ac" "bb" "bc" "cc"
n<-length(c2)
c3<-c();for(i in 1:n){c3<-c(c3,paste(c2[i],letters[ceiling(i/2):3],sep=""))}
c3
[1] "aaa" "aab" "aac" "aba" "abb" "abc" "acb" "acc" "bbb" "bbc" "bcc" "ccc"
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