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 A186111 #54 Oct 26 2023 08:31:05
%S A186111 1,-3,3,-2,5,-9,7,-4,9,-15,11,-6,13,-21,15,-8,17,-27,19,-10,21,-33,23,
%T A186111 -12,25,-39,27,-14,29,-45,31,-16,33,-51,35,-18,37,-57,39,-20,41,-63,
%U A186111 43,-22,45,-69,47,-24,49,-75,51,-26,53,-81,55,-28,57,-87,59,-30,61,-93,63
%N A186111 a(n) = -n if n odd, a(2n) = 3n if n odd, a(4n) = 2n.
%H A186111 G. C. Greubel, <a href="/A186111/b186111.txt">Table of n, a(n) for n = 1..10000</a>
%H A186111 Michael Somos, <a href="http://grail.eecs.csuohio.edu/~somos/rfmc.txt">Rational Function Multiplicative Coefficients</a>.
%H A186111 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (-2,-3,-4,-3,-2,-1).
%F A186111 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 A186111 Euler transform of length 4 sequence [-3, 0, -1, 2].
%F A186111 G.f.: x * (1 - x)^3 * (1 - x^3) / (1 - x^4)^2.
%F A186111 G.f.: x * (1 + x + x^2) * (1 - x)^2 / ((1 + x)^2 * (1 + x^2)^2).
%F A186111 Dirichlet g.f. zeta(s-1)*( 1-5*2^(-s)+4^(1-s)). - _R. J. Mathar_, Mar 31 2011
%F A186111 a(n) = (-1)^(n+1)*n + (-1)^floor(n/2)*A027656(n-2). - _R. J. Mathar_, Mar 31 2011
%F A186111 a(n) = -2*a(n-1) - 3*a(n-2) - 4*a(n-3) - 3*a(n-4) - 2*a(n-5) - a(n-6) with a(1)=1, a(2)=-3, a(3)=3, a(4)=-2, a(5)=5, a(6)=-9. - _Harvey P. Dale_, Aug 08 2012
%F A186111 G.f.: 1/(1+x) - 1/(1+x)^2 - 1/(1+x^2) + 1/(1+x^2)^2. - _Michael Somos_, Apr 24 2015
%F A186111 a(n) = -a(-n) for all n in Z. - _Michael Somos_, Apr 24 2015
%F A186111 G.f.: f(x) - f(x^2) where f(x) := x / (1 + x)^2. - _Michael Somos_, May 07 2015
%F A186111 Moebius transform of A186690. - _Michael Somos_, Apr 25 2015
%F A186111 a(n) = -(-1)^n * A186813(n). - _Michael Somos_, May 07 2015
%F A186111 a(n) = n*cos(n*Pi/2)/2-n*(-1)^n. - _Wesley Ivan Hurt_, May 05 2021
%e A186111 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 A186111 Rest[CoefficientList[Series[x (1-x)^3(1-x^3)/(1-x^4)^2,{x,0,70}],x]] (* or *) LinearRecurrence[{-2,-3,-4,-3,-2,-1},{1,-3,3,-2,5,-9},70] (* _Harvey P. Dale_, Aug 08 2012 *)
%t A186111 a[ n_] := n If[ OddQ[n], 1, -(Mod[n/2, 2] + 1/2)]; (* _Michael Somos_, Apr 25 2015 *)
%t A186111 a[ n_] := n {1, -3/2, 1, -1/2}[[Mod[n, 4, 1]]]; (* _Michael Somos_, Apr 25 2015 *)
%o A186111 (PARI) {a(n) = -(-1)^n * n * [1, 2, 3, 2] [n%4 + 1] / 2};
%o A186111 (PARI) {a(n) = sign(n) * polcoeff( x * (1 - x)^3 * (1 - x^3) / (1 - x^4)^2 + x * O(x^abs(n)), abs(n))};
%o A186111 (PARI) {a(n) = n * if( n%2, 1, -(n/2%2 + 1/2))}; /* _Michael Somos_, Apr 25 2015 */
%o A186111 (Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(x*(1-x)^3*(1-x^3)/(1-x^4)^2)); // _G. C. Greubel_, Aug 14 2018
%Y A186111 Cf. A068073, A186690, A186813.
%K A186111 sign,mult,easy
%O A186111 1,2
%A A186111 _Michael Somos_, Feb 13 2011