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 A134068 #14 Nov 12 2024 18:56:30 %S A134068 0,3,3,6,18,24,60,120,216,480,912,1824,3744,7296,14784,29568,58752, %T A134068 118272,235776,471552,944640,1886208,3775488,7550976,15095808, %U A134068 30203904,60395520,120791040,241606656,483164160,966377472,1932754944,3865411584,7731019776,15461842944 %N A134068 a(n) = 2*a(n-2) + 4*a(n-3), with initial terms 0, 3, 3. %H A134068 Andrew Howroyd, <a href="/A134068/b134068.txt">Table of n, a(n) for n = 0..1000</a> %H A134068 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,4). %F A134068 From _Andrew Howroyd_, Jan 03 2020: (Start) %F A134068 G.f.: 3*x*(1 + x)/((1 - 2*x)*(1 + 2*x + 2*x^2)). %F A134068 a(n) = 3*A134136(n). (End) %o A134068 (PARI) concat([0], Vec(3*(1 + x)/((1 - 2*x)*(1 + 2*x + 2*x^2)) + O(x^40))) \\ _Andrew Howroyd_, Jan 03 2020 %o A134068 (Magma) a:=[0,3,3]; [n le 3 select a[n] else 2*Self(n-2) + 4*Self(n-3):n in [1..35]]; // _Marius A. Burtea_, Jan 03 2020 %o A134068 (Magma) R<x>:=PowerSeriesRing(Integers(), 35); [0] cat Coefficients(R!( 3*x*(1 + x)/((1 - 2*x)*(1 + 2*x + 2*x^2)))); // _Marius A. Burtea_, Jan 03 2020 %Y A134068 Cf. A134136, A038521. %K A134068 nonn %O A134068 0,2 %A A134068 _Paul Curtz_, Jan 29 2008 %E A134068 a(12) corrected and terms a(13) and beyond from _Andrew Howroyd_, Jan 03 2020