As some rishis have written that amavasai tharpanam must be started immediately after 13th day. some rishis have written that after one year you may start amavasya tharpanam. After sapindeekaranam the dead person is mingled with pithrukkal, vaithinatha deekshadeeyam ahneeka kandam -20 says sapindeekaranath orthvam amaa sankramanaadheeshu puthras thilothakam dhthyaath kshethra pindan thathaa charaeth,
As per these words you may do amavasya tharpanam after 13th day, you should not do any sraththam for one year, this has written. this shows only sratham with homam and bhojanam and pinda pradhanam. here in amavasya tharpanam you are doing only tharpanam by using water and black ellu. so you may do amavasya tharpanam from 13th day onwards.