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 A186813 #41 Oct 26 2023 08:30:49
%S A186813 0,1,3,3,2,5,9,7,4,9,15,11,6,13,21,15,8,17,27,19,10,21,33,23,12,25,39,
%T A186813 27,14,29,45,31,16,33,51,35,18,37,57,39,20,41,63,43,22,45,69,47,24,49,
%U A186813 75,51,26,53,81,55,28,57,87,59,30,61,93,63,32,65,99,67,34,69,105,71,36
%N A186813 a(n) = n if n odd, a(2n) = 3n if n odd, a(4n) = 2n.
%H A186813 G. C. Greubel, <a href="/A186813/b186813.txt">Table of n, a(n) for n = 0..10000</a>
%H A186813 Michael Somos, <a href="http://grail.eecs.csuohio.edu/~somos/rfmc.txt">Rational Function Multiplicative Coefficients</a>
%H A186813 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,-3,4,-3,2,-1).
%F A186813 a(n) is multiplicative with a(2) = 3, a(2^e) = 2^(e-1) if e>1, a(p^e) = p^e if p>2.
%F A186813 Euler transform of length 6 sequence [3, -3, 1, 2, 0, -1].
%F A186813 G.f.: x * (1 + x) * (1 + x^3) / ((1 - x) * (1 + x^2))^2.
%F A186813 G.f.: x * (1 - x^2)^3 * (1 - x^6) / ((1 - x)^3 * (1 - x^3) * (1 - x^4)^2). - _Michael Somos_, May 04 2015
%F A186813 G.f.: f(x) - f(-x^2) where f(x) := x/(1-x)^2. - _Michael Somos_, May 04 2015
%F A186813 a(n) = -a(-n) for all n in Z. a(n) = n/2 * A068073(n).
%F A186813 a(n) = n*(4-i^n-(-i)^n)/4 with i=sqrt(-1). - _Bruno Berselli_, Mar 10 2011
%F A186813 a(n) = A134172(n) + A134172(n+1). - _Michael Somos_, May 04 2015
%F A186813 a(n) = -(-1)^n * A186111(n). - _Michael Somos_, May 07 2015
%F A186813 a(n) = n - n*cos(n*Pi/2)/2. - _Wesley Ivan Hurt_, May 05 2021
%F A186813 Dirichlet g.f.: zeta(s-1) * (1 + 1/2^s - 1/4^(s-1)). - _Amiram Eldar_, Oct 26 2023
%e A186813 G.f. = x + 3*x^2 + 3*x^3 + 2*x^4 + 5*x^5 + 9*x^6 + 7*x^7 + 4*x^8 + 9*x^9 + ...
%t A186813 CoefficientList[Series[x(1+x)(1+x^3)/((1-x)(1+x^2))^2,{x,0,80}],x] (* _Harvey P. Dale_, Mar 06 2011 *)
%t A186813 a[ n_] := n/2 {2, 3, 2, 1}[[ Mod[ n, 4, 1]]]; (* _Michael Somos_, May 04 2015 *)
%o A186813 (PARI) {a(n) = n/2 * [1, 2, 3, 2][n%4 + 1]};
%o A186813 (PARI) {a(n) = sign(n) * polcoeff( x * (1 + x) * (1 + x^3) / ((1 - x) * (1 + x^2))^2 + x * O(x^abs(n)), abs(n))};
%o A186813 (Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(x*(1+x)*(1+x^3)/((1-x)*(1+x^2))^2)); // _G. C. Greubel_, Aug 14 2018
%Y A186813 Cf. A068073, A134172, A186111.
%Y A186813 Cf. A187601. - _Bruno Berselli_, Mar 12 2011
%K A186813 nonn,easy,mult
%O A186813 0,3
%A A186813 _Michael Somos_, Feb 27 2011