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A120865
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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 = 12*n^2.
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3
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1, 4, 9, 1, 6, 13, 22, 4, 13, 24, 37, 9, 22, 37, 1, 16, 33, 52, 6, 25, 46, 69, 13, 36, 61, 88, 22, 49, 78, 4, 33, 64, 97, 13, 46, 81, 118, 24, 61, 100, 141, 37, 78, 121, 9, 52, 97, 144, 22, 69, 118, 169, 37, 88, 141, 1, 54, 109, 166, 16, 73, 132, 193, 33, 94, 157, 222, 52
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| The j's that match these k's comprise A120864.
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REFERENCES
| 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) 1-17.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..10000
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FORMULA
| a(n) = -3*n^2+[1+n*sqrt(3)]^2, where [ ]=floor.
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EXAMPLE
| 1=-3*1+[1+sqrt(3)]^2
4=-3*4+[1+2*sqrt(3)]^2
9=-3*9+[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.
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PROG
| (MAGMA) [-3*n^2+Floor(1+n*Sqrt(3))^2: n in [1..70]]; // Vincenzo Librandi, Sep 13 2011
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CROSSREFS
| Cf. A120864.
Sequence in context: A007892 A010297 A001191 * A133868 A199788 A197266
Adjacent sequences: A120862 A120863 A120864 * A120866 A120867 A120868
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KEYWORD
| nonn
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu), Jul 09 2006
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