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A165727
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.
2
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
OFFSET
0,8
COMMENTS
A synopsis of the denominators of the transitions in the Rydberg-Ritz spectrum of hydrogenic atoms.
LINKS
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, ...
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);
CROSSREFS
Cf. A165441 (top row and left column removed)
Sequence in context: A216060 A230278 A190113 * A284609 A363174 A290448
KEYWORD
nonn,tabl,frac,easy
AUTHOR
Paul Curtz, Sep 25 2009
EXTENSIONS
Edited by R. J. Mathar, Feb 27 2010, Mar 03 2010
STATUS
approved