# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/

Search: id:a123010
Showing 1-1 of 1

%I A123010 #27 Jul 14 2021 16:02:20
%S A123010 1,0,4,16,84,416,2084,10416,52084,260416,1302084,6510416,32552084,
%T A123010 162760416,813802084,4069010416,20345052084,101725260416,508626302084,
%U A123010 2543131510416,12715657552084,63578287760416,317891438802084
%N A123010 a(n) = 5*a(n-1) + a(n-2) - 5*a(n-3), for n>4, with a(1)=1, a(2)=0, a(3)=4, a(4)=16.
%H A123010 G. C. Greubel, <a href="/A123010/b123010.txt">Table of n, a(n) for n = 1..1000</a>
%H A123010 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,1,-5).
%F A123010 O.g.f.: (1 -4*x -x^2)/((1+x)*(1-5*x)). - _R. J. Mathar_, Dec 05 2007
%F A123010 a(n) = (1/3)*(2*5^(n-2) - 2*(-1)^n) + (1/5)*0^(n-1). - _Ridouane Oudra_, Feb 22 2021
%F A123010 E.g.f.: (1/75)*(48 + 158x - 50*exp(-x) + 2*exp(5*x)). - _G. C. Greubel_, Jul 13 2021
%t A123010 LinearRecurrence[{5,1,-5}, {1,0,4,16}, 40] (* _G. C. Greubel_, Jul 13 2021 *)
%o A123010 (PARI) my(x='x+O('x^33)); Vec((x^2+4*x-1)/((x+1)*(5*x-1))) \\ _Joerg Arndt_, Feb 22 2021
%o A123010 (Sage) [1]+[(2/3)*(5^(n-2) - (-1)^n) for n in (2..40)] # _G. C. Greubel_, Jul 13 2021
%K A123010 nonn,easy
%O A123010 1,3
%A A123010 _Roger L. Bagula_, Sep 23 2006
%E A123010 Edited by _N. J. A. Sloane_, Oct 15 2006
%E A123010 Edited by _Joerg Arndt_, Feb 22 2021

# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE