OFFSET
1,1
COMMENTS
The j's that match these k's comprise A120866.
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(1 + n*sqrt(5))^2.
EXAMPLE
4 = -5*1 + floor(1 + sqrt(5))^2,
5 = -5*4 + floor(1 + 2*sqrt(5))^2,
4 = -5*9 + floor(1 + 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(1+n*Sqrt(5))^2: n in [1..70]]; // Vincenzo Librandi, Sep 13 2011
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jul 09 2006
STATUS
approved