R moving average between data frame variables

I am trying to find a solution but haven't, yet. I have a dataframe structured as follows:

country City 2014 2015 2016 2017 2018 2019
France  Paris 23   34   54   12   23   21
US       NYC   1    2    2    12   95  54 

I want to find the moving average for every 3 years (i.e. 2014-16, 2015-17, etc) to be placed in ad-hoc columns.

country City 2014 2015 2016 2017 2018 2019 2014-2016  2015-2017  2016-2018  2017-2019
France  Paris 23   34   54   12   23   21    37          33.3      29.7        18.7  
US       NYC   1    2    2    12   95  54    etc           etc     etc          etc

Any hint?