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Search: id:A120865
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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
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OFFSET
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1,2
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COMMENT
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The j's that match these k's comprise A120864.
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REFERENCES
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C. Kimberling, The equation (j+k+1)^2-4k=Q*n^2 and related dispersions, preprint.
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FORMULA
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a(n)=-3*n^2+[1+n*sqrt(3)]^2, where [ ]=Floor.
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EXAMPLE
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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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CROSSREFS
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Cf. A120864.
Sequence in context: A007892 A010297 A001191 this_sequence A133868 A070438 A070638
Adjacent sequences: A120862 A120863 A120864 this_sequence A120866 A120867 A120868
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu), Jul 09 2006
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