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A061041 Numerator of 1/16 - 1/n^2. 23
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
4,2
COMMENTS
From Brackett spectrum of hydrogen. 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. 78.
LINKS
Frederick Sumner Brackett, Visible and Infra-Red Radiation of Hydrogen Astrophysical Journal, 56, No. 3 (1922) pp. 154-161.
J. J. O'Connor and E. F. Robertson, Johannes Robert Rydberg
Eric Weisstein's World of Physics, Balmer Formula
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).
FORMULA
a(4*n+6) = A078371(n). - Paul Curtz, Oct 05 2008
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
a(n) = (n^2-16) / gcd(16*n^2, n^2-16). - Franklin T. Adams-Watters, Sep 25 2011, corrected by Colin Barker, Jan 13 2014.
MAPLE
A061041:=n->numer(1/16 - 1/n^2); seq(A061041(n), n=4..60); # Wesley Ivan Hurt, Jan 28 2014
MATHEMATICA
Numerator/@(1/16-1/Range[4, 60]^2) (* Harvey P. Dale, Mar 24 2011 *)
PROG
(PARI) a(n)=numerator(1/16-1/n^2) \\ Charles R Greathouse IV, Aug 17 2011
(Haskell)
import Data.Ratio ((%), numerator)
a061041 n = numerator (1%16 - 1%n^2) -- Reinhard Zumkeller, May 30 2012
(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
CROSSREFS
Sequence in context: A180878 A146282 A117911 * A248308 A035417 A038295
KEYWORD
nonn,frac,nice,easy
AUTHOR
N. J. A. Sloane, May 26 2001
STATUS
approved

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Last modified April 22 17:24 EDT 2024. Contains 371905 sequences. (Running on oeis4.)