R forecast: Handling a cutted frequency of a time series [35 months instead of 36]

Question

I'm dealing with the following problem right now: I'm going through Data Smart Forecasting example with this data set:

library(forecast)
mydata <- c(165, 171, 147, 143, 164, 160, 152, 150, 159, 169, 173, 203, 169, 166, 162, 147, 188, 161, 162, 169, 185, 188, 200, 229, 189, 218, 185, 199, 210, 193, 211, 208, 216, 218, 264, 304)
mydata.ts <- ts(mydata, frequency = 12, start = c(2010, 1))
mydata.forecast <- forecast(mydata.ts)
plot(mydata.forecast)

With this code, I produce a Holt-Winters Forecast, just like the book says. Now I was wondering I could forecast month #36 (value = 304) by only using 35 previous observations.

mydata1 <- c(165, 171, 147, 143, 164, 160, 152, 150, 159, 169, 173, 203, 169, 166, 162, 147, 188, 161, 162, 169, 185, 188, 200, 229, 189, 218, 185, 199, 210, 193, 211, 208, 216, 218, 264)
mydata1.ts <- ts(mydata1, frequency = 12, start = c(2010, 1))
mydata1.forecast <- forecast(mydata1.ts)
plot(mydata1.forecast)

This does not produce a forecast with trend and seasonality, but a simple constant level forecast.

mydata1.forecast$mean
Jan      Feb      Mar      Apr      May      Jun      Jul      Aug
2012                                                                        
2013 239.1952 239.1952 239.1952 239.1952 239.1952 239.1952 239.1952 239.1952
2014 239.1952 239.1952 239.1952 239.1952 239.1952 239.1952 239.1952 239.1952
Sep      Oct      Nov      Dec
2012                            239.1952
2013 239.1952 239.1952 239.1952 239.1952
2014 239.1952 239.1952 239.1952

I have an intuition that cutting a time series such that

elements in time series / modulo 12 != 0 

results in a falsified forecast. But how could I overcome this problem?

I also tried to cut the first 11 observations so that the time series contains 24 elements

mydatacut <- c(203, 169, 166, 162, 147, 188, 161, 162, 169, 185, 188, 200, 229, 189, 218, 185, 199, 210, 193, 211, 208, 216, 218, 264)
mydatacut.ts <- ts(mydatacut, frequency = 12, start = c(2010, 1))
mydatacut.forecast <- forecast(mydatacut.ts)
plot(mydatacut.forecast)
mydatacut.forecast$mean

Jan     Feb     Mar     Apr     May     Jun     Jul     Aug     Sep
2012 240.437 240.437 240.437 240.437 240.437 240.437 240.437 240.437 240.437
2013 240.437 240.437 240.437 240.437 240.437 240.437 240.437 240.437 240.437
Oct     Nov     Dec
2012 240.437 240.437 240.437
2013 240.437 240.437 240.437

So this does not help either.

Every hint and suggestion is highly appreciated.