Journal of Integer Sequences, Vol. 10 (2007), Article 07.2.6

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.

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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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