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 A137444 #23 May 18 2025 19:47:32 %S A137444 1,4,6,4,-4,-16,-24,-16,16,64,96,64,-64,-256,-384,-256,256,1024,1536, %T A137444 1024,-1024,-4096,-6144,-4096,4096,16384,24576,16384,-16384,-65536, %U A137444 -98304,-65536,65536,262144,393216,262144,-262144,-1048576,-1572864,-1048576,1048576 %N A137444 a(n) = 2*a(n-1) - 2*a(n-2) with a(0)=1, a(1)=4. %C A137444 Sequence opposite to its second differences. %C A137444 Degenerate case of a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) with n > 3 (for which the sequence is identical to its fourth differences). %H A137444 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-2). %F A137444 G.f.: (1+2*x)/(1-2*x+2*x^2). - _Colin Barker_, Mar 28 2012 %F A137444 a(n) = (1/2 + 3*i/2)*(1 - i)^n + (1/2 - 3*i/2)*(1 + i)^n, n >= 0, where i=sqrt(-1). - _Taras Goy_, Apr 20 2019 %o A137444 (Magma) m:=41; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+2*x)/(1-2*x+2*x^2))); // _Bruno Berselli_, Mar 28 2012 %K A137444 sign,easy %O A137444 0,2 %A A137444 _Paul Curtz_, Apr 18 2008 %E A137444 More terms from _Bruno Berselli_, Mar 28 2012