Geodesic
The Connell sum sequence
Journal of integer sequences, Tome 10 (2007) no. 2
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.
Classification : 05C78, 11B25, 11B99
Keywords: connell sequence, connell (m, r)-sequence, gamma-labeling 
@article{JIS_2007__10_2_a5,
     author = {Bullington,  Grady D.},
     title = {The {Connell} sum sequence},
     journal = {Journal of integer sequences},
     year = {2007},
     volume = {10},
     number = {2},
     zbl = {1121.05101},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2007__10_2_a5/}
}
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Bullington,  Grady D. The Connell sum sequence. Journal of integer sequences, Tome 10 (2007) no. 2. http://geodesic.mathdoc.fr/item/JIS_2007__10_2_a5/