Using TTR package to calculate Exponential moving average

To get the answer you are looking for you would need to write

TTR::EMA(1:20, n=1,  ratio=2/(5+1))

 [1]  1.000000  1.333333  1.888889  2.592593  3.395062  4.263374  5.175583
 [8]  6.117055  7.078037  8.052025  9.034683 10.023122 11.015415 12.010276
[15] 13.006851 14.004567 15.003045 16.002030 17.001353 18.000902

If you call TTR::EMA(1:20, n=5) it is equivalent to calling

TTR::EMA(1:20, n=5, ratio=2/(5+1))

This will put NA's in the first 4 places and then the 5th place will be the simple mean of the first 5 entries. (i.e. 3 in this case). Then the EMA algorithm will start. The 6th place will be 6 * 2 / 6 + 3 * 4 / 6 = 4. The 7th place will be 7 * 2 / 6 + 4 * 4 / 6 = 5. Etc...

You can see the exact algorithm here

TTR::EMA calculates the first non-missing value as the arithmetic mean of the first n variables, then begins calculating recursively. You can match your calculation by setting n=1 and ratio=1/3.

R> EMA(x,n=1,ratio=1/3)
 [1]  1.000000  1.333333  1.888889  2.592593  3.395062  4.263374  5.175583
 [8]  6.117055  7.078037  8.052025  9.034683 10.023122 11.015415 12.010276
[15] 13.006851 14.004567 15.003045 16.002030 17.001353 18.000902