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A165727
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Table T(k,n) read by antidiagonals: denominator of 1/min(n,k)^2 -1/max(n,k)^2 with T(0,n) = T(k,0) = 0.
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2
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0, 0, 0, 0, 1, 0, 0, 4, 4, 0, 0, 9, 1, 9, 0, 0, 16, 36, 36, 16, 0, 0, 25, 16, 1, 16, 25, 0, 0, 36, 100, 144, 144, 100, 36, 0, 0, 49, 9, 225, 1, 225, 9, 49, 0, 0, 64, 196, 12, 400, 400, 12, 196, 64, 0, 0, 81, 64, 441, 144, 1, 144, 441, 64, 81, 0, 0, 100, 324, 576, 784, 900, 900, 784, 576, 324, 100, 0
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OFFSET
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0,8
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COMMENTS
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A synopsis of the denominators of the transitions in the Rydberg-Ritz spectrum of hydrogenic atoms.
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..1034
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EXAMPLE
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... A000004
0, 1, 4, 9, 16, 25, 36, 49, 64, 81, ... A000290
0, 4, 1, 36, 16, 100, 9, 196, 64, 324, ... A061038
0, 9, 36, 1, 144, 225, 12, 441, 576, 81, ... A061040
0, 16, 16, 144, 1, 400, 144, 784, 64, 1296, ... A061042
0, 25, 100, 225, 400, 1, 900, 1225, 1600, 2025, ... A061044
0, 36, 9, 12, 144, 900, 1, 1764, 576, 324, ... A061046
0, 49, 196, 441, 784, 1225, 1764, 1, 3136, 3969, ... A061048
0, 64, 64, 576, 64, 1600, 576, 3136, 1, 5184, ... A061050
0, 81, 324, 81, 1296, 2025, 324, 3969, 5184, 1, ...
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MAPLE
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T:= (k, n)-> `if` (n=0 or k=0, 0, denom (1/min (n, k)^2 -1/max (n, k)^2)):
seq (seq (T (k, d-k), k=0..d), d=0..11);
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CROSSREFS
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Cf. A165441 (top row and left column removed)
Sequence in context: A216060 A230278 A190113 * A284609 A290448 A282593
Adjacent sequences: A165724 A165725 A165726 * A165728 A165729 A165730
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KEYWORD
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nonn,tabl,frac,easy
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AUTHOR
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Paul Curtz, Sep 25 2009
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EXTENSIONS
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Edited by R. J. Mathar, Feb 27 2010, Mar 03 2010
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STATUS
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approved
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