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A120867
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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 = 20*n^2.
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3
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4, 5, 4, 1, 19, 16, 11, 4, 36, 29, 20, 9, 55, 44, 31, 16, 76, 61, 44, 25, 4, 80, 59, 36, 11, 101, 76, 49, 20, 124, 95, 64, 31, 149, 116, 81, 44, 5, 139, 100, 59, 16, 164, 121, 76, 29, 191, 144, 95, 44, 220, 169, 116, 61, 4, 196, 139, 80, 19, 225, 164, 101, 36, 256, 191
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The j's that match these k's comprise A120866.
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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) = -5*n^2+[1+n*sqrt(5)]^2, where [ ]=floor.
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EXAMPLE
| 4=-5*1+[1+sqrt(5)]^2,
5=-5*4+[1+2*sqrt(5)]^2,
4=-5*9+[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.
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PROG
| (MAGMA) [-5*n^2+Floor(1+n*Sqrt(5))^2: n in [1..70]]; // Vincenzo Librandi, Sep 13 2011
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CROSSREFS
| Cf. A120866.
Sequence in context: A071992 A174984 A092141 * A011427 A175622 A071413
Adjacent sequences: A120864 A120865 A120866 * A120868 A120869 A120870
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KEYWORD
| nonn
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu), Jul 09 2006
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