Journal of Integer Sequences, Vol. 18 (2015), Article 15.1.8

Finite Sequences Dominated by the Squares

L. Haddad
120 rue de Charonne
75011 Paris

C. Helou
Department of Mathematics
Pennsylvania State University
25 Yearsley Mill Road
Media, PA 19063


We evaluate the number u(n) of length-n finite sequences (ak)1 ≤ kn of natural numbers that satisfy the inequality akk2 for all k. We thus determine two recurrence relations for u(n) by two different methods, and we give an explicit expression in closed form for it.

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(Concerned with sequence A242105.)

Received August 24 2014; revised versions received September 2 2014; January 12 2015. Published in Journal of Integer Sequences, January 13 2015.

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