Here's one way... there's probably a slicker way to do it, but this is the best I could figure out 
library(tidyverse)
partridge <- rep(1,12)
dove <- c(0, rep(2,11))
hen <- c(rep(0,2), rep(3,10))
bird <- c(rep(0,3), rep(4,9))
ring <- c(rep(0,4), rep(5,8))
geese <- c(rep(0,5), rep(6,7))
swan <- c(rep(0,6), rep(7,6))
maid <- c(rep(0,7), rep(8,5))
ladies <- c(rep(0,8), rep(9,4))
lords <- c(rep(0,9), rep(10,3))
pipers <- c(rep(0,10), rep(11,2))
drummers <- c(rep(0,11), rep(12,1))
christmas <- as.data.frame(cbind(partridge, dove, hen, bird, ring, geese, swan, maid, ladies, lords, pipers, drummers))
christmasCount <- christmas %>% summarize_all(list(sum = sum)) %>% pivot_longer(cols = 1:12, names_to = "gift")