Chapter 15 Calculating the nth Term in the Perrin Sequence when n is Prime

Based on the results of Chapters 13 and 14 an equation is developed to calculate directly the value of Perrin(N) when N is a prime number and where Perrin(n) is given from the sequence P(n) = P(n-2) + P(n-3) with P(1) = 0, P(2) = 2, P(3) = 3.
A modified incomplete Beta function is derived to calculate each term of the Sigma1 orbit but these terms can be further simplified to a short sequence in (A,B) where A and B have been previously defined. The Perrin sequence can also be expressed as a hypergeometric function.

Calculation of the Perrin Sequence with a Modified Beta Function_