Journal of Integer Sequences, Vol. 6 (2003), Article 03.1.4

The Integer Sequence A002620 and Upper Antagonistic Functions


Sam E. Speed
Department of Mathematical Sciences
University of Memphis
Memphis, TN 38152-3240
USA

Abstract: 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.

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(Concerned with sequence A002620 .)

Received January 10 2001; revised versions received March 19 2002; February 26, 2003. Published in Journal of Integer Sequences March 2, 2003.

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