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 A168056 #15 Sep 08 2022 08:45:48 %S A168056 1,1,3,5,5,7,9,9,11,13,13,15,17,17,19,21,21,23,25,25,27,29,29,31,33, %T A168056 33,35,37,37,39,41,41,43,45,45,47,49,49,51,53,53,55,57,57,59,61,61,63, %U A168056 65,65,67,69,69,71,73,73,75,77,77,79,81,81,83,85,85,87,89,89,91,93,93 %N A168056 Expansion of (1+2*x^2+x^3)/((1-x)^2*(1+x+x^2)). %H A168056 G. C. Greubel, <a href="/A168056/b168056.txt">Table of n, a(n) for n = 0..1000</a> %H A168056 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1). %F A168056 G.f.: (1+2*x^2+x^3)/((1-x)^2*(1+x+x^2)). %F A168056 a(n) = A168057(n)/2^n. %F A168056 a(n) = (12*n+3+6*cos(2*n*Pi/3)-2*sqrt(3)*sin(2*n*Pi/3))/9. - _Wesley Ivan Hurt_, Sep 30 2017 %t A168056 LinearRecurrence[{1, 0, 1, -1}, {1, 1, 3, 5}, 100] (* _G. C. Greubel_, Jul 07 2016 *) %t A168056 CoefficientList[Series[(1 + 2 x^2 + x^3) / ((1 - x)^2 (1 + x + x^2)), {x, 0, 80}], x] (* _Vincenzo Librandi_, Jul 08 2016 *) %o A168056 (Magma) I:=[1,1,3,5]; [n le 4 select I[n] else Self(n-1)+Self(n-3)-Self(n-4): n in [1..70]]; // _Vincenzo Librandi_, Jul 08 2016 %Y A168056 Cf. A168053. %K A168056 easy,nonn %O A168056 0,3 %A A168056 _Paul Barry_, Nov 17 2009