OFFSET
1,2
COMMENTS
The k's that match these j's comprise A120867.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Clark Kimberling, The equation (j+k+1)^2-4*k=Q*n^2 and related dispersions, Journal of Integer Sequences, 10 (2007), Article #07.2.7.
FORMULA
a(n) = 5*n^2 - floor(n*sqrt(5))^2.
EXAMPLE
1 = 5*1 - floor(sqrt(5))^2,
4 = 5*4 - floor(2*sqrt(5))^2,
9 = 5*9 - floor(3*sqrt(5))^2, etc.
Moreover,
for n = 1, the unique (j,k) is (1,4): (1 + 4 + 1)^2 - 4*4 = 20*1;
for n = 2, the unique (j,k) is (4,5): (4 + 5 + 1)^2 - 4*5 = 20*4;
for n = 3, the unique (j,k) is (9,4): (9 + 4 + 1)^2 - 4*4 = 20*9.
PROG
(Magma) [5*n^2-Floor(n*Sqrt(5))^2: n in [1..70]]; // Vincenzo Librandi, Sep 13 2011
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jul 09 2006
STATUS
approved