|
Search: id:A120868
|
|
|
| A120868 |
|
a(n) is the number k for which there exists a unique pair (j,k) of positive integers such that (j+k+1)^2-4*k=5*n^2. |
|
+0
1
|
|
| 1, 4, 1, 5, 11, 4, 11, 1, 9, 19, 5, 16, 29, 11, 25, 4, 19, 36, 11, 29, 1, 20, 41, 9, 31, 55, 19, 44, 5, 31, 59, 16, 45, 76, 29, 61, 11, 44, 79, 25, 61, 4, 41, 80, 19, 59, 101, 36, 79, 11, 55, 101, 29, 76, 1, 49, 99, 20, 71, 124, 41, 95, 9, 64, 121, 31, 89, 149, 55, 116, 19, 81, 145
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
The j's that match these k's comprise A005752.
|
|
REFERENCES
|
C. Kimberling, The equation (j+k+1)^2-4k=Q*n^2 and related dispersions, preprint.
|
|
FORMULA
|
Let r=(1/2)*sqrt(5). If n is odd, then a(n)=([n*r+1/2]+ 1/2)^2-(5/4)*n^2; if n is even, then a(n)=(1+[n*r])^2-(5/4)*n^2, where [ ]=Floor.
|
|
EXAMPLE
|
1=([r+1/2]+ 1/2)^2-(5/4)*1^2,
4=(1+[2*r])^2-(5/4)*2^2,
1=([3*r+1/2]+ 1/2)^2-(5/4)*3^2, etc. Moreover,
for n=1, the unique (j,k) is (1,1): (1+1+1)^2-4*1=5*1;
for n=2, the unique (j,k) is (1,4): (1+4+1)^2-4*4=5*4;
for n=3, the unique (j,k) is (5,1): (5+1+1)^2-4*1=5*9.
|
|
CROSSREFS
|
Cf. A005752.
Sequence in context: A139356 A080852 A090842 this_sequence A100279 A132379 A130746
Adjacent sequences: A120865 A120866 A120867 this_sequence A120869 A120870 A120871
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Clark Kimberling (ck6(AT)evansville.edu), Jul 09 2006
|
|
|
Search completed in 0.002 seconds
|
