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 A181880 #18 Sep 18 2015 12:23:09
%S A181880 1,4,19,89,417,1954,9156,42903,201034,942001,4414009,20683073,
%T A181880 96916320,454128508,2127946065,9971086104,46722311119,218930448853,
%U A181880 1025859814873,4806952917170,22524321562152,105544004814991,494555936863590,2317380083461485,10858732149251701,50881624784254849,238420075668235984,1117183909174960184,5234877488488803537,24529481757148330684
%N A181880 Expansion of 1/(1-4*x-3*x^2-x^3).
%C A181880 B(n):=a(n-2)*(-1)^n, B(0):=0, B(1):=0, (o.g.f. x^2/(1 + 4*x + 3*x^2 -x^3))appears in the following formula for the nonpositive powers of rho*sigma, where rho:=2*cos(Pi/7) and sigma:=sin(3*Pi/7)/sin(Pi/7) = rho^2-1 are the ratios of the smaller and larger diagonal length to the side length in a regular 7-gon (heptagon). See the Steinbach reference where the basis <1,rho,sigma> is used in an extension of the rational field. (rho*sigma)^(-n) = C(n) + B(n)*rho + A(n)*sigma,n>=0, with C(n)= A085810(n)*(-1)^n, and A(n)= A116423(n+1)*(-1)^(n+1). For the nonnegative powers see A120757(n), |A122600(n-1)| and A181879(n), respectively. See also a comment under A052547.
%H A181880 P. Steinbach, <a href="http://www.jstor.org/stable/2691048">Golden fields: a case for the heptagon</a>, Math. Mag. 70 (1997), no. 1, 22-31.
%H A181880 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4, 3, 1).
%F A181880 O.g.f.: 1/(1-4*x-3*x^2-x^3).
%F A181880 a(n) = 4*a(n) + 3*a(n-2) +a(n-3), n>=2, a(-1):=0, a(0)=1, a(1)=4.
%t A181880 CoefficientList[Series[1/(1-4*x-3*x^2-x^3),{x,0,40}],x] (* or *) LinearRecurrence[{4,3,1},{1,4,19},40] (* _Vladimir Joseph Stephan Orlovsky_, Feb 01 2012 *)
%K A181880 nonn,easy
%O A181880 0,2
%A A181880 _Wolfdieter Lang_, Nov 27 2010