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The Connell Sum Sequence
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Grady D. Bullington

Department of Mathematics

University of Wisconsin, Oshkosh

Oshkosh, Wisconsin 54901

USA

**Abstract:**

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.

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(Concerned with sequences
A001614
A045928
A045929
A045930
A122793
A122794
A122795
A122796
A122797
A122798
A122799 and
A122800
.)

Received October 27 2006;
revised version received January 22 2007.
Published in *Journal of Integer Sequences*, January 23 2007.

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