Geodesic
The equation \((j+k+1)^2-4k = Qn^2\) and related dispersions
Journal of integer sequences, Tome 10 (2007) no. 2
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},
     year = {2007},
     volume = {10},
     number = {2},
     zbl = {1117.11015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2007__10_2_a3/}
}
TY  - JOUR
AU  - Kimberling,  Clark
TI  - The equation \((j+k+1)^2-4k = Qn^2\) and related dispersions
JO  - Journal of integer sequences
PY  - 2007
VL  - 10
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/JIS_2007__10_2_a3/
LA  - en
ID  - JIS_2007__10_2_a3
ER  - 
%0 Journal Article
%A Kimberling,  Clark
%T The equation \((j+k+1)^2-4k = Qn^2\) and related dispersions
%J Journal of integer sequences
%D 2007
%V 10
%N 2
%U http://geodesic.mathdoc.fr/item/JIS_2007__10_2_a3/
%G en
%F JIS_2007__10_2_a3
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/