Comparing the values of a certain number previous rows with the current row

In a database containing firm and patent class values, I want to calculate the following variables:

Technological abandonment: Number of previously active technological patent classes abandoned annually.

Specifically, I want to create variables that calculate the number of patent classes (variable = class) that the firm (id = gvkey) has used in the past 3 years (t-3, t-2, and t-1) (min observation of one year prior is acceptable if the firm history initially doesn't have 3 years) but are missing in this year (t)I would like to do the same with a 5 year window as well

I have a dataset containing millions of rows, so a fast data.table solution is much preferred

In the following dataset:

df <- data.table(year=c(1979,1979,1980,1980,1981,1981,1982,1983,1983,1984,1984),                 category = c("A","A","B","C","A","D","F","F","C","A","B"))

The desired outcome would be (for a three year window):

    year        class tech_aband_3 1: 1979        A     0 2: 1979        A     0 3: 1980        B     1 4: 1980        C     1 5: 1981        A     2 6: 1981        D     2 7: 1982        F     4 8: 1983        F     3 9: 1983        C     310: 1984        A     311: 1984        B     3

Many thanks in advance.