cp's OEIS Frontend

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.

A106851 Expansion of (-3*x^3 - 7*x^2 + 2*x)/((1-4*x-x^2)*(1-4*x+x^2)).

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%I A106851 #18 Dec 26 2022 04:54:17
%S A106851 0,2,9,37,152,626,2585,10701,44400,184610,769065,3209461,13415048,
%T A106851 56153618,235357241,987609501,4148575200,17443003202,73402179657,
%U A106851 309116995525,1302649664888,5492768393906,23173154692697,97810060234605
%N A106851 Expansion of (-3*x^3 - 7*x^2 + 2*x)/((1-4*x-x^2)*(1-4*x+x^2)).
%H A106851 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (8, -16, 0, 1).
%F A106851 G.f.: (-3*x^3 - 7*x^2 + 2*x)/((1-4*x-x^2)*(1-4*x+x^2)).
%F A106851 a(n) = (1/2) * [A001834(n-1) + Fibonacci(3n+1) ]. - _Ralf Stephan_, Nov 18 2010
%F A106851 a(0)=0, a(1)=2, a(2)=9, a(3)=37, a(n)=8*a(n-1)-16*a(n-2)+a(n-4) [_Harvey P. Dale_, Aug 05 2011]
%t A106851 CoefficientList[Series[(-3 x^3-7x^2+2x)/((1-4x-x^2)(1-4x+x^2)),{x,0,30}],x] (* or *) LinearRecurrence[{8,-16,0,1},{0,2,9,37},31] (* _Harvey P. Dale_, Aug 05 2011 *)
%K A106851 nonn,easy
%O A106851 0,2
%A A106851 _Roger L. Bagula_, May 30 2005
%E A106851 Edited by _N. J. A. Sloane_, Apr 09 2007
%E A106851 New name from _Joerg Arndt_, Dec 26 2022