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A120073
Denominator triangle for hydrogen spectrum rationals.
12
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
OFFSET
2,1
COMMENTS
The corresponding numerator triangle is A120072.
See A120072 and A120070 for more details.
FORMULA
a(m,n) = denominator(r(m,n)) with r(m,n) = 1/n^2 - 1/m^2, m>=2, n=1..m-1.
EXAMPLE
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;
MATHEMATICA
Table[(1/n^2 - 1/m^2)//Denominator, {m, 2, 15}, {n, m-1}]//Flatten (* Jean-François Alcover, Sep 16 2013 *)
PROG
(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)
flatten([[A120073(n, k) for k in range(1, n)] for n in range(2, 19)]) # G. C. Greubel, Apr 24 2023
CROSSREFS
Row sums give A120075.
Sequence in context: A134815 A367992 A352002 * A056894 A272145 A272221
KEYWORD
nonn,easy,tabl,frac
AUTHOR
Wolfdieter Lang, Jul 20 2006
STATUS
approved