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 A165441 Table T(k,n) read by antidiagonals: denominator of 1/min(n,k)^2 -1/max(n,k)^2. 4
 1, 4, 4, 9, 1, 9, 16, 36, 36, 16, 25, 16, 1, 16, 25, 36, 100, 144, 144, 100, 36, 49, 9, 225, 1, 225, 9, 49, 64, 196, 12, 400, 400, 12, 196, 64, 81, 64, 441, 144, 1, 144, 441, 64, 81, 100, 324, 576, 784, 900, 900, 784, 576, 324, 100, 121, 25, 81, 64, 1225, 1, 1225, 64, 81, 25, 121 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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 = 1..1035 FORMULA T(n,k) = A165727(n,k). EXAMPLE .1, 4, 9, 16, 25, 36, 49, 64, 81, ... A000290 .4, 1, 36, 16, 100, 9, 196, 64, 324, ... A061038 .9, 36, 1, 144, 225, 12, 441, 576, 81, ... A061040 16, 16, 144, 1, 400, 144, 784, 64, 1296, ... A061042 25, 100, 225, 400, 1, 900, 1225, 1600, 2025, ... A061044 36, 9, 12, 144, 900, 1, 1764, 576, 324, ... A061046 49, 196, 441, 784, 1225, 1764, 1, 3136, 3969, ... A061048 64, 64, 576, 64, 1600, 576, 3136, 1, 5184, ... A061050 81, 324, 81, 1296, 2025, 324, 3969, 5184, 1, ... MAPLE T:= (k, n)-> denom(1/min (n, k)^2 -1/max (n, k)^2): seq(seq(T(k, d-k), k=1..d-1), d=2..12); MATHEMATICA T[n_, k_] := Denominator[1/Min[n, k]^2 - 1/Max[n, k]^2]; Table[T[n-k, k], {n, 2, 12}, {k, 1, n-1}] // Flatten (* Jean-François Alcover, Feb 04 2020 *) CROSSREFS Sequence in context: A176441 A363683 A143183 * A204997 A178840 A246668 Adjacent sequences: A165438 A165439 A165440 * A165442 A165443 A165444 KEYWORD nonn,tabl,frac,look,easy AUTHOR Paul Curtz, Sep 19 2009 EXTENSIONS Edited by R. J. Mathar, Feb 27 2010, Mar 03 2010 STATUS approved

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Last modified October 4 20:53 EDT 2023. Contains 365888 sequences. (Running on oeis4.)