Chapter 34- Calculus of Integer Sequences


Pursue some path, however narrow and crooked, in which you can walk with love and reverence – Thoreau

All sequences representing monic cubic polynomials are shown to be generated by a single formula based on two modified Tribonacci sequences.  These representations are multi-variable polynomials in x, y, and z and increase in the number of monomial terms with n. It is shown that these polynomials are continuous and can be integrated and differentiated.  These inter-sequence polynomials (ISPs) obey the fundamental theorem of calculus and are graphically shown as surface sheets.  Each sheet represents a set of sequences and are connected to the fundamental sequences described by Perrin, Lucas and Narayana and elemental repeated sequences. Sheets can be individual laminae or multiple sheets which may intersect other sheets.

Calculus of Integer Sequences_