Forecasting seasonality with Fourier terms in R

I am using the auto.arima from the forecast package in R to determine the optimal K-terms for fourier series.

After I do that, I want to then calculate the seasonality and plug that one seasonality variable into a multiple regression model.

Using the gas dataset from the forecast package, I was able to extract the optimal amount of fourier terms:

library(forecast)

##Public dataset from the forecast package

##Choose Optimal Amount of K-Terms
bestfit <- list(aicc=Inf)
for(i in 1:6)
{
fit <- auto.arima(gas, xreg=fourier(gas, K=i), seasonal=FALSE)
if(fit$$aicc < bestfit$$aicc)
bestfit <- fit
else break;
optimal_k_value<-max(i)
print(i)
}

##Extract Fourier Terms
seasonality<-data.frame(fourier(gas, K=optimal_k_value))

##Convert Gas TS Data to Dataframe
gas_df <- data.frame(gas, year = trunc(time(gas)),
month = month.abb[cycle(gas)])

##Extract True Seasonality by Taking Sum of Rows
seasonality$total<- rowSums(seasonality) ##Combine Seasonality to Month and Year final_df<-cbind(gas_df, seasonality$total)


Would the seasonality\$total column be considered by "seasonality variable" for later modelling or do I need to add coefficients to it?