FFT of a stretched vector
Conceptually you should split this into two steps

Up-sample by a factor of 3, i.e. x = [a 0 0 b 0 0 ...]. This results in a 3 times periodic repetition of the spectrum.
Convolve with a rectangular pulse of length three, i.e. h = [1 1 1]. This crates time stretched sequence you want. Convolution in time is multiplication in frequency, your three copies of the original spectrum get multiplied with a $sinc$ function.