Fibonacci sequence is actually Virahahka sequence

  • This note is to make accessible the explanation advanced by Virahanka as rationale for his sequence in the context of prosody. It is to state that what is known as Fibonacci sequence is actually Virahahka sequence.

This note presents Virahāṅka’s original proof of the sequence associated with prosody that is now known variously as the Virahāṅka-Fibonacci sequence, Fibonacci sequence, or just the Virahāṅka sequence. This sequence is also seen as the number of arrangements of beads in a necklace of a certain value, where each bead has the value of 1 or 2. 


This sequence was implicitly known as early as fourth to second century BCE in the work of Piṅgala, and was formally derived by Virahāṅka about 600 years before Fibonacci and, therefore, the last name is appropriate. The proof given here leads easily to the generalization of the Nārāyaṇa sequence.


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