Samvatsara

Samvatsara (संवत्सर) is a Sanskrit term for a "year" in Vedic literature such as the "Rigveda" and other ancient texts. In the medieval era literature, a samvatsara refers to the "Jovian year", that is a year based on the relative position of the planet Jupiter, while the solar year is called "varsha". A jovian year is not equal to a solar year based on the relative position of Earth and Sun. A Jovian year is defined in Indian calendars as the time Brihaspati (Jupiter) takes to transit from one constellation to the next relative to its mean motion.
There are 60 samvatsara mentioned in the historic Indian calendars, and these are called "Brihaspati samvatsara chakra". These are not numbered but each has been given a name. Once all 60 samvatsaras are over, the cycle starts over again. 
Omitted Samvatsaras.
The ancient text "Surya Siddhanta" calculates the Jovian year to be about 361.026721 days or about 4.232 days shorter than the Earth-based solar year. This difference requires that about once every 85 solars years (~ 86 jovian years), one of the named samvatsara is expunged (skipped as a shadow year), to synchronize the two calendars. 
This system of omission has fallen into disuse in South India. "There is evidence to show that the cycle of Jupiter was in use in Southern India before Saka 828 (A.D. 905-6); but from that year, according to the Arya Siddhanta, or from Saka 831 (A.D. 908-9) according to the Sürya-Siddhanta, the expunction of the samvatsaras was altogether neglected, with the result that the 60-year cycle in the south became luni-solar from that year." 
List of Samvatsaras.
The sixty Samvatsaras are divided into 3 groups of 20 Samvatsaras each. The first 20 from "Prabhava" to "Vyaya" are assigned to Brahma. The next 20 from "Sarvajit" to "Parabhava" to Vishnu and the last 20 to Shiva.