A <- rbind(c(0,0,0,0,127,4,80),
           c(.6747,.737,0,0,0,0,0),
           c(0,.0486,.661,0,0,0,0),
           c(0,0,.0147,.6907,0,0,0),
           c(0,0,0,.0518,0,0,0),
           c(0,0,0,0,.8091,0,0),
           c(0,0,0,0,0,.8091,.8089))

# the matrix power function
matrix.power <- function(n, A) {
  out <- A
  for (i in 1:(n-1))
    out <- out %*% A
  return(out)
}

matrix.power(2, A)
matrix.power(3, A)
matrix.power(4, A)
matrix.power(5, A)
matrix.power(6, A)
matrix.power(37, A)