valid.counts <- function(l,cvec,x){
  vec = seq(cvec[1])
  lst = lapply(numeric(l), function(i) vec)
  mat = as.matrix(expand.grid(lst))

  partial = NULL
  for (k in seq(l-1)){
    for (r in seq(l-k+1)){
      #print(paste(k,r,sep= " "))
      partial = c(which(rowSums(mat[,r:(r+k-1),drop=FALSE])<=cvec[k]),partial)
    }
  }

  mat[which(rowSums(mat[unique(partial),])==x),]
}

n = 20
c1 = 15
c2 = 22
x = 35
s = 0
for (i in 0:c1){
  for (j in 0:c1){
    for (k in 0:c1){
      if (i+j<=c2 & j+k<=c2 & i+j+k==x){
        s = s+choose(n,i)*choose(n,j)*choose(n,k)
        print(paste(i,j,k,sep = " "))
      }
    }
  }
}