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 A061039 Numerator of 1/9 - 1/n^2. 34
 0, 7, 16, 1, 40, 55, 8, 91, 112, 5, 160, 187, 8, 247, 280, 35, 352, 391, 16, 475, 520, 7, 616, 667, 80, 775, 832, 11, 952, 1015, 40, 1147, 1216, 143, 1360, 1435, 56, 1591, 1672, 65, 1840, 1927, 224, 2107, 2200, 85, 2392, 2491, 32, 2695, 2800, 323, 3016, 3127 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,2 COMMENTS The denominators are given in A061040. From Paschen 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 = 3..1000 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1). FORMULA a(n) <= n^2 - 9; if n is not divisible by 3 then a(n) = n^2 - 9. - Stefan Steinerberger, Apr 16 2006 a(n) = 3*a(n-27) - 3*a(n-54) + a(n-81) for n > 83. - Colin Barker, Oct 09 2016 a(n) = (n^2 - 9)/9^2 if n == 3 or 24 (mod 27), a(n) = (n^2 - 9)/(3*9) if n == 6 or 24 or 15 or 21 (mod 27), a(n) = (n^2 - 9)/9 if n == 0  (mod 9) and n^2 - 9 otherwise. From  the period length 27 sequence gcd(n^2 - 9, 9*n^2). - Wolfdieter Lang, Mar 15 2018 MAPLE A061039:=n->numer(1/9-1/n^2): seq(A061039(n), n=3..80); # Wesley Ivan Hurt, Apr 12 2017 MATHEMATICA Table[Numerator[1/9 - 1/n^2], {n, 3, 60}] (* Stefan Steinerberger, Apr 16 2006 *) PROG (Haskell) import Data.Ratio ((%), numerator) a061039 n = numerator \$ 1%9 - 1%n ^ 2  -- Reinhard Zumkeller, Jan 03 2012 (PARI) a(n)=numerator(1/9-1/n^2) \\ Charles R Greathouse IV, Nov 20 2012 CROSSREFS Cf. A061035..A061050. Sequence in context: A087485 A156377 A069526 * A258771 A063593 A070417 Adjacent sequences:  A061036 A061037 A061038 * A061040 A061041 A061042 KEYWORD nonn,frac,nice,easy AUTHOR N. J. A. Sloane, May 26 2001 STATUS approved

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Last modified October 16 06:26 EDT 2019. Contains 328050 sequences. (Running on oeis4.)