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A061041 Numerator of 1/16 - 1/n^2. 24
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

Reinhard Zumkeller, Table of n, a(n) for n = 4..10000

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

CROSSREFS

Cf. A061035 - A061050, A078371, A064038.

Sequence in context: A180878 A146282 A117911 * A248308 A035417 A038295

Adjacent sequences:  A061038 A061039 A061040 * A061042 A061043 A061044

KEYWORD

nonn,frac,nice,easy

AUTHOR

N. J. A. Sloane, May 26 2001

STATUS

approved

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Last modified November 19 11:04 EST 2017. Contains 294936 sequences.