A general algorithm is discussed based on the total number of bonding and non-bonding partitions into parts of arbitrary integer modulus. The  bonding partitions introduces the Padovan sequence from the Perrin sequence of numbers. The Padovan sequence is shown as a representation of the partition of integers into odd parts. A method for calculating the Padovan number expressing each  basis representations as bonding and non bonding integers mod 5 is developed.

Chapter 18 _A General Algorithm and Perrin and Padovan Sequences