OFFSET
1,2
COMMENTS
The j's that match these k's comprise A120864.
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) = -3*n^2 + floor(1 + n*sqrt(3))^2.
EXAMPLE
1 = -3*1 + floor(1 + sqrt(3))^2,
4 = -3*4 + floor(1 + 2*sqrt(3))^2,
9 = -3*9 + floor(1 + 3*sqrt(3))^2, etc.
Moreover,
for n = 1, the unique (j,k) is (2,1): (2+1+1)^2 - 4*1 = 12*1;
for n = 2, the unique (j,k) is (3,4): (3+4+1)^2 - 4*4 = 12*4;
for n = 3, the unique (j,k) is (2,9): (2+9+1)^2 - 4*9 = 12*9.
PROG
(Magma) [-3*n^2+Floor(1+n*Sqrt(3))^2: n in [1..70]]; // Vincenzo Librandi, Sep 13 2011
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jul 09 2006
STATUS
approved