How to repeat codes changing the variables in a sequence in R - r

Question

This is the code I want to repeat
A_1981 <- Base[1:12]]
B <- sum(A_1981)
MFI_1981 <- sum(A_1981^2)/B
Base is a Raster brick
A_1981 is for a year
MFI_1981 is the final result
So i have to continue with the next year
A_1982 <- Base[13:24]]
B <- sum(A_1982)
MFI_1982 <- sum(A_1982^2)/B
To repeat the same code I think in replace values only in the names:
a <- seq(1,421,by=12)
b <- seq(12,432,by=12)
c <- seq(1981,2016, by=1)
And do it in sequence for the next third year, would be something like this
A_a[3] <- Base[[b[3]:c[3]]
B <- sum(A_a[3])
MFI_a[3] <- sum(A_[3]^2)/B
Have to be some way with for or make a function. But have no idea where to start.

Answer 1

I think you are looking for something like this
Example data (48 layers, i.e, 4 "years")
library(raster)
f <- system.file("external/rlogo.grd", package="raster")
Base <- stack(rep(f, 4*4))
Approach 1
f <- function(year) {
start <- (year-1981) * 12 + 1
A <- Base[[start:(start+11)]]
sum(A^2)/sum(A)
}
mfi <- lapply(1981:1984, f)
MFI <- stack(mfi)
Approach 2
for (year in 1981:1984) {
start <- (year-1981) * 12 + 1
A <- Base[[start:(start+11)]]
mfi <- sum(A^2)/sum(A)
writeRaster(mfi, paste0(year, ".tif"))
}
s <- stack(paste0(1981:1984, ".tif"))
Approach 3, with mapply as in Rui Barradas' answer, but fixed for when Base is a RasterBrick (and also including the last year)
n <- nlayers(Base)
a <- seq(1, n, by = 12)
mfi <- mapply(function(i, j) sum(Base[[i:j]]^2)/sum(Base[[i:j]]), a, a+11)
s <- stack(mfi)

Answer 2

The following does what you want using mapply and creates only one object in the .GlobalEnv, which I named MFI.
I start by creating a vector Base, since you have not posted a dataset example.
set.seed(2469) # Make the results reproducible
n <- 432
Base <- sample(100, n, TRUE)
step <- 12
b <- seq(1 + step, n, by = step)
a <- seq(1, n - step, by = step)
MFI <- mapply(function(i, j) sum(Base[i:j]^2)/sum(Base[i:j]), a, b)
head(MFI)
#[1] 63.66472 70.54014 67.60567 53.15550 58.71111 65.37008
Another way would be to use Map, like #Parfait suggests in his comment.
obj <- Map(function(i, j) sum(Base[i:j]^2)/sum(Base[i:j]), a, b)
names(obj) <- paste("MFI", 1980 + seq_along(obj), sep = "_")
obj$MFI_1981
#[1] 63.66472
Note that length(obj) is 35 and therefore the last obj is obj$MFI_2015 and not MFI_2016 like is said in the question. This can be easily solved by making n <- 444 right at the beginning of the code.