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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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS A synopsis of the denominators of the transitions in the Rydberg-Ritz spectrum of hydrogenic atoms. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1034 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 A290448 A282593 Adjacent sequences:  A165724 A165725 A165726 * A165728 A165729 A165730 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

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Last modified April 21 07:13 EDT 2021. Contains 343146 sequences. (Running on oeis4.)