1,1

This sequence results from A087059 by deleting duplicates.

C. Kimberling, The equation (j+k+1)^2-4k=Q*n^2 and related dispersions, preprint.

For each positive integer n, there is a unique pair (j,k) of

positive integers such that (j+k+1)^2-4*k=8*n^2. This

representation is used to define the fixed-k dispersion for Q=8,

given by A120861, having northwest corner

1 7 41 239

2 12 70 408

3 19 111 647

4 24 140 816

The pair (j,k) for each n, shown in the position occupied by

n in the above array, is shown here:

(1,2) (17,2) (43,2) (673,2)

(4,1) (32,1) (196,1) (1152,1)

(2,7) (46,7) (306,7) (1822,7)

(7,4) (63,4) (391,4) (2303,4)

The fixed-k for row 1 is a(1)=2;

the fixed-k for row 2 is a(2)=1; etc.

(For example, (46+7+1)^2-4*7=8*19^2.)

Cf. A087059, A120861.

Sequence in context: A075085 A124048 A087059 this_sequence A019642 A048505 A124821

Adjacent sequences: A120869 A120870 A120871 this_sequence A120873 A120874 A120875

nonn

Clark Kimberling (ck6(AT)evansville.edu), Jul 10 2006