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Search: id:A061037
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| A061037 |
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Numerator of 1/4 - 1/n^2. |
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+0
45
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| 0, 5, 3, 21, 2, 45, 15, 77, 6, 117, 35, 165, 12, 221, 63, 285, 20, 357, 99, 437, 30, 525, 143, 621, 42, 725, 195, 837, 56, 957, 255, 1085, 72, 1221, 323, 1365, 90, 1517, 399, 1677, 110, 1845, 483, 2021, 132, 2205, 575, 2397, 156, 2597, 675
(list; graph; listen)
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OFFSET
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2,2
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COMMENT
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From Balmer spectrum of hydrogen. Wavelengths in hydrogen spectrum are given by Rydberg's formula 1/wavelength = constant*(1/m^2 - 1/n^2).
a(n)= mix (A142705=A026741(n)*A026741(n+2)) , (A078371=A005408(n)*A005408(n+2)). Note A026741=mix A001477 , A005408. a(4n)=A001477(n)*A001477(n+1). [From Paul Curtz (bpcrtz(AT)free.fr), Aug 27 2009]
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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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Harry J. Smith, Table of n, a(n) for n=2,...,1000
J. J. O'Connor and E. F. Robertson, Johannes Robert Rydberg
Eric Weisstein's World of Physics, Balmer Formula
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FORMULA
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G.f.: x^2(-3x^11-x^10-3x^9+14x^7+6x^6+30x^5+2x^4+21x^3+3x^2+5x)/(1-x^4)^3.
a(4n+2) = n(n+1), a(2n+3) = (2n+1)(2n+5), a(4n+4) = (2n+1)(2n+3). - Ralf Stephan, Jun 10 2005
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PROGRAM
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(PARI) { for (n=2, 1000, write("b061037.txt", n, " ", numerator(1/4 - 1/n^2)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 17 2009]
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CROSSREFS
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Cf. A061035-A061050.
Cf. A126252.
Sequence in context: A092525 A101367 A049457 this_sequence A070262 A084183 A099730
Adjacent sequences: A061034 A061035 A061036 this_sequence A061038 A061039 A061040
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KEYWORD
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nonn,frac,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), May 26 2001
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