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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
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,8
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COMMENTS
| A synopsis of the denominators of the transitions in the Rydberg-Ritz spectrum of hydrogenic atoms.
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LINKS
| Alois P. Heinz, Table of n, a(n) for n = 0..1034
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EXAMPLE
| 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
| 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
| Cf. A165441 (top row and left column removed)
Sequence in context: A143266 A133845 A190113 * A075866 A202168 A156450
Adjacent sequences: A165724 A165725 A165726 * A165728 A165729 A165730
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KEYWORD
| nonn,tabl,frac,easy
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AUTHOR
| Paul Curtz (bpcrtz(AT)free.fr), Sep 25 2009
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EXTENSIONS
| Edited by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 27 2010, Mar 03 2010
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