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A061041
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Numerator of 1/16 - 1/n^2.
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23
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0, 9, 5, 33, 3, 65, 21, 105, 1, 153, 45, 209, 15, 273, 77, 345, 3, 425, 117, 513, 35, 609, 165, 713, 3, 825, 221, 945, 63, 1073, 285, 1209, 5, 1353, 357, 1505, 99, 1665, 437, 1833, 15, 2009, 525, 2193, 143, 2385, 621, 2585, 21, 2793, 725
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OFFSET
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4,2
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COMMENTS
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From Brackett spectrum of hydrogen. Wavelengths in hydrogen spectrum are given by Rydberg's formula 1/wavelength = constant*(1/m^2 - 1/n^2).
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REFERENCES
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J. E. Brady and G. E. Humiston, General Chemistry, 3rd. ed., Wiley; p. 78.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,3,0,0,0,0,0,0,0, -6,0,0,0,0,0,0,0,10,0,0,0,0,0,0,0,-12,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0, -10,0,0,0,0,0,0,0,6,0,0,0,0,0,0,0,-3,0,0,0,0,0,0,0,1).
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FORMULA
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a(n) = 3*a(n-8) - 6*a(n-16) + 10*a(n-24) - 12*a(n-32) + 12*a(n-40) - 10*a(n-48) + 6*a(n-56) - 3*a(n-64) + a(n-72). - Charles R Greathouse IV, Aug 17 2011
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MAPLE
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MATHEMATICA
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PROG
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(Haskell)
import Data.Ratio ((%), numerator)
(Magma) [Numerator(1/16 -1/n^2): n in [4..60]]; // G. C. Greubel, Apr 19 2023
(SageMath) [numerator(1/16 -1/n^2) for n in range(4, 61)] # G. C. Greubel, Apr 19 2023
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CROSSREFS
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KEYWORD
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nonn,frac,nice,easy
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AUTHOR
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STATUS
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approved
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