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 A146535 #40 Feb 15 2025 09:47:33
%S A146535 1,1,5,7,3,11,13,5,17,19,7,23,25,9,29,31,11,35,37,13,41,43,15,47,49,
%T A146535 17,53,55,19,59,61,21,65,67,23,71,73,25,77,79,27,83,85,29,89,91,31,95,
%U A146535 97,33,101,103,35,107,109,37,113,115,39,119,121,41,125,127,43,131,133,45
%N A146535 Numerator of (2*n-1)/3.
%C A146535 From _Jaroslav Krizek_, May 28 2010: (Start)
%C A146535 a(n+1) = numerators of antiharmonic mean of the first n positive integers for n >= 1.
%C A146535 See A169609(n-1) - denominators of antiharmonic mean of the first n positive integers for n >= 1. (End)
%H A146535 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,2,0,0,-1).
%F A146535 From _R. J. Mathar_, Nov 21 2008: (Start)
%F A146535 a(n) = 2*a(n-3) - a(n-6).
%F A146535 G.f.: x(1+x)(1+5x^2+x^4)/((1-x)^2*(1+x+x^2)^2). (End)
%F A146535 Sum_{k=1..n} a(k) ~ (7/9) * n^2. - _Amiram Eldar_, Apr 04 2024
%F A146535 a(n) = (2*n - 1)*(7 - A061347(n) +3*A102283(n))/9. - _Stefano Spezia_, Feb 14 2025
%e A146535 Fractions begin with 1/6, 1/2, 5/6, 7/6, 3/2, 11/6, 13/6, 5/2, 17/6, 19/6, 7/2, 23/6, ...
%t A146535 Table[Numerator[(2 n - 1)/6], {n, 1, 100}]
%t A146535 LinearRecurrence[{0,0,2,0,0,-1},{1,1,5,7,3,11},100] (* _Harvey P. Dale_, Feb 24 2015 *)
%o A146535 (PARI) a(n) = numerator((2*n-1)/3); \\ _Altug Alkan_, Apr 13 2018
%Y A146535 Cf. A146306, A146307, A146308, A146309, A146310, A146311, A146312, A146313.
%Y A146535 Cf. A061347, A102283.
%Y A146535 Trisections: A016921, A005408, A016969. [_R. J. Mathar_, Nov 21 2008]
%K A146535 nonn,easy,frac
%O A146535 1,3
%A A146535 _Artur Jasinski_, Oct 31 2008
%E A146535 Name edited by _Altug Alkan_, Apr 13 2018