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A120073
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Denominator triangle for hydrogen spectrum rationals.
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12
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4, 9, 36, 16, 16, 144, 25, 100, 225, 400, 36, 9, 12, 144, 900, 49, 196, 441, 784, 1225, 1764, 64, 64, 576, 64, 1600, 576, 3136, 81, 324, 81, 1296, 2025, 324, 3969, 5184, 100, 25, 900, 400, 100, 225, 4900, 1600, 8100, 121, 484, 1089, 1936, 3025, 4356, 5929, 7744, 9801, 12100
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OFFSET
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2,1
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COMMENTS
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The corresponding numerator triangle is A120072.
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LINKS
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FORMULA
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a(m,n) = denominator(r(m,n)) with r(m,n) = 1/n^2 - 1/m^2, m>=2, n=1..m-1.
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EXAMPLE
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For the rational triangle see W. Lang link.
Denominator triangle begins as:
4;
9, 36;
16, 16, 144;
25, 100, 225, 400;
36, 9, 12, 144, 900;
49, 196, 441, 784, 1225, 1764;
64, 64, 576, 64, 1600, 576, 3136;
81, 324, 81, 1296, 2025, 324, 3969, 5184;
100, 25, 900, 400, 100, 225, 4900, 1600, 8100;
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MATHEMATICA
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Table[(1/n^2 - 1/m^2)//Denominator, {m, 2, 15}, {n, m-1}]//Flatten (* Jean-François Alcover, Sep 16 2013 *)
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PROG
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(Magma) [Denominator(1/k^2 - 1/n^2): k in [1..n-1], n in [2..18]]; // G. C. Greubel, Apr 24 2023
(SageMath)
def A120073(n, k): return denominator(1/k^2 - 1/n^2)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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