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 A138749 #21 Jun 21 2025 11:44:08
%S A138749 -1,-7,-9,17,79,73,-249,-863,-481,3353,9111,1457,-42641,-92567,28071,
%T A138749 518977,897599,-799687,-6087369,-8176303,14084239,69049993,67678791,
%U A138749 -209892383,-758178721,-466895527,2857102551,8048682737,1811852719,-36619708247
%N A138749 a(n) = 2*a(n-1) - 5*a(n-2), with a(1) = -1, a(2) = -7.
%H A138749 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-5).
%F A138749 a(n) = 2*a(n-1) - 5*a(n-2), n>3.
%F A138749 a(n) = left term in [1,-2; 2,1]^n * [1,1].
%F A138749 O.g.f.: -x*(1+5*x)/(1-2*x+5*x^2). a(n)=-A045873(n)-5*A045873(n-1). - _R. J. Mathar_, Apr 03 2008
%F A138749 a(n) = (1/2)*(1+i)*((1+2*i)^n-i*(1-2*i)^n), where i=sqrt(-1). - _Bruno Berselli_, Jul 06 2011
%e A138749 a(5) = 79 = 2*a(4) - 5*a(3) = 2*17 - 5*(-9).
%e A138749 a(5) = 79 = left term in [1,-2, 2,1]^5.
%t A138749 Rest[CoefficientList[Series[-x*(1+5*x)/(1-2*x+5*x^2),{x,0,30}],x]] (* or *) LinearRecurrence[{2,-5},{-1,-7},30] (* _James C. McMahon_, Jun 21 2025 *)
%o A138749 (PARI) a(n)={local(v=Vec((1+2*I*x)^n)); sum(k=1,#v, real(v[k])-imag(v[k]));} /* cf. A116483 */ /* _Joerg Arndt_, Jul 06 2011 */
%K A138749 sign,easy
%O A138749 1,2
%A A138749 _Gary W. Adamson_, Mar 28 2008