If you are counting Amavasya tharpanam by English months, you have more problems than seeing tharpanam as the only way to pay homage to your ancestors....Members have to perform Ammavasai two times in the month
of January 2014 - one on the very first day of month (year!)
and the other one on 30th (Thursday).
Consequently, there is no Ammavasai during Feb 2014.