Geodesic
The equation $(j+k+1)^2-4k = Qn^2$ and related dispersions
Journal of integer sequences, Tome 10 (2007) no. 2.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Suppose $Q$ is a positive nonsquare integer congruent to 0 or 1 mod 4. Then for every positive integer $n$, there exists a unique pair $(j,k) of positive integers such that (j+k+1)$^2-4k = Qn^2$ . This representation is used to generate the fixed-$j$ array for $Q$ and the fixed-$k$ array for $Q$. These arrays are proved to be dispersions; i.e., each array contains every positive integer exactly once and has certain compositional and row-interspersion properties.$
Classification : 11B37, 11D09, 11D85
Keywords: Beatty sequence, complementary equation, dispersion, interspersion, pell equation, recurrences 
@article{JIS_2007__10_2_a3,
     author = {Kimberling, Clark},
     title = {The equation $(j+k+1)^2-4k = Qn^2$ and related dispersions},
     journal = {Journal of integer sequences},
     publisher = {mathdoc},
     volume = {10},
     number = {2},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2007__10_2_a3/}
}
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Kimberling, Clark. The equation $(j+k+1)^2-4k = Qn^2$ and related dispersions. Journal of integer sequences, Tome 10 (2007) no. 2. http://geodesic.mathdoc.fr/item/JIS_2007__10_2_a3/