cumulative frequency given certain conditions in R

I am new at R and I do not really know how to count cumulative number of occurrences of a row if it is the same ID but different date.Also, if the first date appears more than once, it should not count in the first attempt.Look at the rows 2 and 3, that is why the column I am trying to build is called "count" and equals to zero. "count" represents the times that the id has appeared but it follows the next two rules:

1.If it is the first appearence of the Id ever, it assigns zero. For example, for Id 1 despite there are two different registers for the very first date of this Id, "count" equals zero.

2.For the next Id 1 appereance (row 3 of Id1 ) it has a different date, that is why "count" equals 2. Because the 01/01/2018 Id1 appeared twice.

This is the DT and the result that I am looking for is in the "count" column:

We can use dplyr to group_by id and return 0 for the first date else return the count of occurrence of 1st date

library(dplyr)

df %>%
  group_by(id) %>%
  mutate(count = ifelse(date == date[1L], 0, sum(date == date[1L])))

#     id   date       count
#   <dbl> <fct>      <dbl>
#1     1 01/01/2018     0
#2     1 01/01/2018     0
#3     1 02/01/2018     2
#4     2 03/02/2018     0
#5     2 04/04/2018     1

Or using base R ave with similar logic

as.numeric(with(df, ave(date, id, FUN = function(x) 
           ifelse(x == x[1L], 0, sum(x == x[1L])))))
#[1] 0 0 2 0 1

data

df <- data.frame(id = c(1, 1, 1, 2, 2), date = c("01/01/2018", "01/01/2018", 
     "02/01/2018", "03/02/2018", "04/04/2018"), stringsAsFactors = FALSE)