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 A086341 #26 Sep 14 2022 02:01:54
%S A086341 1,3,3,5,7,9,15,17,31,33,63,65,127,129,255,257,511,513,1023,1025,2047,
%T A086341 2049,4095,4097,8191,8193,16383,16385,32767,32769,65535,65537,131071,
%U A086341 131073,262143,262145,524287,524289,1048575,1048577,2097151,2097153
%N A086341 a(n) = 2*2^floor(n/2) - (-1)^n.
%H A086341 Vincenzo Librandi, <a href="/A086341/b086341.txt">Table of n, a(n) for n = 0..2000</a>
%H A086341 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-1,2,2).
%F A086341 E.g.f.: 2*cosh(sqrt(2)*x) + 2*sinh(sqrt(2)*x)/sqrt(2) - sinh(x) + cosh(x).
%F A086341 a(n) = (1 + 1/sqrt(2))*sqrt(2)^n + (1 - 1/sqrt(2))*(-sqrt(2))^n - (-1)^n.
%F A086341 G.f.: (1+2*x)^2/((1+x)*(1-2*x^2)). - _Colin Barker_, Aug 17 2012
%F A086341 a(n) = a(n-1) + 2*a(n-2) + 2*a(n-3); a(0)=1, a(1)=3, a(2)=3. - _Harvey P. Dale_, Mar 10 2013
%F A086341 From _Amiram Eldar_, Sep 14 2022: (Start)
%F A086341 Sum_{n>=0} 1/a(n) = A065442 + A323482 - 1/2.
%F A086341 Sum_{n>=0} (-1)^n/a(n) = 2 * A248721. (End)
%t A086341 CoefficientList[Series[(1+2x)^2/((1+x)(1-2x^2)),{x,0,50}],x] (* or *) LinearRecurrence[ {-1,2,2},{1,3,3},50] (* _Harvey P. Dale_, Mar 10 2013 *)
%o A086341 (Magma) [2*2^Floor(n/2)-(-1)^n: n in [0..40]]; // _Vincenzo Librandi_, Aug 16 2011
%o A086341 (PARI) vector(40, n, n--; 2^(floor(n/2)+1) - (-1)^n) \\ _G. C. Greubel_, Nov 08 2018
%Y A086341 Cf. A016116 (2^floor(n/2)).
%Y A086341 Cf. A065442, A248721, A323482.
%K A086341 easy,nonn
%O A086341 0,2
%A A086341 _Paul Barry_, Jul 16 2003