The Integer Sequence A002620 and Upper Antagonistic Functions

This paper shows the equivalence of various integer functions to the integer sequence A002620, and to the maximum of the product of certain pairs of combinatorial or graphical invariants. This maximum is the same as the upper bound of the Nordhaus-Gaddum inequality and related to Turán’s number. The computer algebra program MAPLE is used for solutions of linear recurrence and differential equations in some of the proofs. Chapter three of The Encyclopedia of Integer Sequences by Sloane and Plouffe describes the usefulness of apparently different expressions of an integer sequence. Define brc, the floor of r, to be the largest integer less than or equal to a real number r, and dre, the ceiling of r, the smallest integer greater than or equal to r. For manipulations of floor and ceiling operations, see chapter three of [20], and for graph theory terms see [10, 13, 21].