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 A061036 Triangle T(m,n) = denominator of 1/m^2 - 1/n^2, n >= 1, m=n,n-1,n-2,...,1. 3
 1, 1, 4, 1, 36, 9, 1, 144, 16, 16, 1, 400, 225, 100, 25, 1, 900, 144, 12, 9, 36, 1, 1764, 1225, 784, 441, 196, 49, 1, 3136, 576, 1600, 64, 576, 64, 64, 1, 5184, 3969, 324, 2025, 1296, 81, 324, 81, 1, 8100, 1600, 4900, 225, 100, 400, 900, 25, 100, 1, 12100, 9801 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Wavelengths in hydrogen spectrum are given by Rydberg's formula 1/wavelength = constant*(1/m^2 - 1/n^2). REFERENCES J. E. Brady and G. E. Humiston, General Chemistry, 3rd. ed., Wiley; p. 77. LINKS _Reinhard Zumkeller_, Rows n=..100 of triangle, flattened J. J. O'Connor and E. F. Robertson, Johannes Robert Rydberg Eric Weisstein's World of Physics, Balmer Formula EXAMPLE Triangle 1/m^2-1/n^2, m >= 1, 1<=n<=m, (i.e. with rows reversed) begins 0 3/4, 0 8/9, 5/36, 0 15/16, 3/16, 7/144, 0 24/25, 21/100, 16/225, 9/400, 0 35/36, 2/9, 1/12, 5/144, 11/900, 0 MATHEMATICA t[m_, n_] := Denominator[1/m^2 - 1/n^2]; Table[t[m, n], {n, 1, 12}, {m, n, 1, -1}] // Flatten (* Jean-François Alcover, Oct 17 2012 *) PROG (Haskell) import Data.Ratio ((%), denominator) a061036 n k = a061036_tabl !! (n-1) !! (k-1) a061036_row = map denominator . balmer where    balmer n = map (subtract (1 % n ^ 2) . (1 %) . (^ 2)) [n, n-1 .. 1] a061036_tabl = map a061036_row [1..] -- Reinhard Zumkeller, Apr 12 2012 CROSSREFS Cf. A061035. Rows give A061037-A061050. Cf. A126252. Sequence in context: A144284 A144285 A091741 * A217020 A144267 A011801 Adjacent sequences:  A061033 A061034 A061035 * A061037 A061038 A061039 KEYWORD nonn,tabl,easy,nice,frac AUTHOR N. J. A. Sloane, May 26 2001 EXTENSIONS More terms from Naohiro Nomoto, Jul 15 2001 STATUS approved

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Last modified June 19 11:40 EDT 2013. Contains 226404 sequences.