The Connell Sum Sequence
Grady D. Bullington
Department of Mathematics
University of Wisconsin, Oshkosh
Oshkosh, Wisconsin 54901
The Connell sum sequence refers to the
partial sums of the Connell sequence. In this paper, the Connell
sequence, Connell sum sequence and generalizations from Iannucci and
Mills-Taylor are interpreted as sums of
elements of triangles, relating them to polygonal number-stuttered
arithmetic progressions. The n-th element of the Connell sum
sequence is established as a sharp upper bound for the value of a
gamma-labeling of a graph of size n. The limiting behavior and a
explicit formula for the Connell (m,r)-sum sequence are also given.
Full version: pdf,
(Concerned with sequences
Received October 27 2006;
revised version received January 22 2007.
Published in Journal of Integer Sequences, January 23 2007.
Journal of Integer Sequences home page