This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A061045 #28 Mar 03 2023 16:51:39 %S A061045 -35,-2,-1,-5,-11,0,13,7,5,4,85,1,133,10,7,55,253,2,325,91,5,28,493,5, %T A061045 589,40,77,187,805,2,925,247,13,70,1189,35,1333,88,55,391,1645,4,1813, %U A061045 475,221,130,2173,7,2365,154,95,667,2773,20,2989,775,119,208,3445,11,3685,238,437,1015,4189,10 %N A061045 Numerator of 1/36 - 1/n^2. %C A061045 Sixth case of Rydberg's formula. From Humphrey's spectrum of hydrogen. See A045944, A000567, A061043, A061046, A061047. - _Paul Curtz_, Dec 08 2008 %H A061045 Reinhard Zumkeller, <a href="/A061045/b061045.txt">Table of n, a(n) for n = 1..10000</a> %H A061045 Curtis J. Humphreys, <a href="https://doi.org/10.1364/JOSA.42.000432">The Sixth Series in the Hydrogen Spectrum</a>, Journal of the Optical Society of America, 1952, 42, p. 432. %e A061045 The fractions are -35/36, -2/9, -1/12, -5/144, -11/900, 0, 13/1764, 7/576, 5/324, 4/225, 85/4356, 1/48, 133/6084, 10/441, 7/300, 55/2304, 253/10404, 2/81, 325/12996, ... %t A061045 Numerator[(1/36-1/Range[100]^2)] (* _Harvey P. Dale_, Mar 17 2013 *) %o A061045 (Haskell) %o A061045 import Data.Ratio ((%), numerator) %o A061045 a061045 = numerator . (1 % 36 -) . recip . (^ 2) . fromIntegral %o A061045 -- _Reinhard Zumkeller_, Jan 06 2014 %o A061045 (Magma) [Numerator(1/6^2 -1/n^2): n in [1..80]]; // _G. C. Greubel_, Feb 24 2023 %o A061045 (SageMath) %o A061045 def A061045(n): return ((n^2-36)/(6*n)^2).numerator() %o A061045 [A061045(n) for n in range(1,81)] # _G. C. Greubel_, Feb 24 2023 %Y A061045 A061046 gives denominators. %Y A061045 Cf. A000567, A045944, A061035 - A061050. %K A061045 sign,frac %O A061045 1,1 %A A061045 _N. J. A. Sloane_, May 26 2001