Search: id:A061037
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%I A061037
%S A061037 0,5,3,21,2,45,15,77,6,117,35,165,12,221,63,285,20,357,99,437,30,
%T A061037 525,143,621,42,725,195,837,56,957,255,1085,72,1221,323,1365,90,
%U A061037 1517,399,1677,110,1845,483,2021,132,2205,575,2397,156,2597,675
%N A061037 Numerator of 1/4 - 1/n^2.
%C A061037 From Balmer spectrum of hydrogen. Wavelengths in hydrogen spectrum are 
               given by Rydberg's formula 1/wavelength = constant*(1/m^2 - 1/n^2).
%C A061037 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]
%D A061037 J. E. Brady and G. E. Humiston, General Chemistry, 3rd. ed., Wiley; p. 
               78.
%H A061037 Harry J. Smith, <a href="b061037.txt">Table of n, a(n) for n=2,...,1000</
               a>
%H A061037 J. J. O'Connor and E. F. Robertson, <a href="http://www-groups.dcs.st-andrews.ac.uk/
               ~history/Mathematicians/Rydberg.html">Johannes Robert Rydberg</a>
%H A061037 Eric Weisstein's World of Physics, <a href="http://scienceworld.wolfram.com/
               physics/BalmerFormula.html">Balmer Formula</a>
%F A061037 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.
%F A061037 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
%o A061037 (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]
%Y A061037 Cf. A061035-A061050.
%Y A061037 Cf. A126252.
%Y A061037 Sequence in context: A092525 A101367 A049457 this_sequence A070262 A084183 
               A099730
%Y A061037 Adjacent sequences: A061034 A061035 A061036 this_sequence A061038 A061039 
               A061040
%K A061037 nonn,frac,nice
%O A061037 2,2
%A A061037 N. J. A. Sloane (njas(AT)research.att.com), May 26 2001

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