cp's OEIS Frontend

A190441 a(n) = 4*a(n-1) + 39*a(n-2), with a(0)=0, a(1)=1.

%I A190441 #30 Sep 08 2022 08:45:57
%S A190441 0,1,4,55,376,3649,29260,259351,2178544,18828865,160278676,1375440439,
%T A190441 11752630120,100652697601,860963365084,7369308666775,63054805905376,
%U A190441 539622261625729,4617626476812580,39515774110653751,338150529038305624,2893717306468718785
%N A190441 a(n) = 4*a(n-1) + 39*a(n-2), with a(0)=0, a(1)=1.
%H A190441 Bruno Berselli, <a href="/A190441/b190441.txt">Table of n, a(n) for n = 0..300</a>
%H A190441 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,39).
%F A190441 G.f.: x/(1-4*x-39*x^2).
%F A190441 a(n) = ((2+sqrt(43))^n - (2-sqrt(43))^n)/(2*sqrt(43)).
%t A190441 a = {0, 1}; Do[AppendTo[a, 4 a[[-1]] + 39 a[[-2]]], {20}]; a (* _Bruno Berselli_, Dec 26 2012 *)
%t A190441 CoefficientList[Series[x / (1 - 4 x - 39 x^2), {x, 0, 25}], x] (* _Vincenzo Librandi_, Aug 19 2013 *)
%t A190441 LinearRecurrence[{4,39},{0,1},30] (* _Harvey P. Dale_, Aug 21 2021 *)
%o A190441 (Maxima) a[0]:0$ a[1]:1$ a[n]:=4*a[n-1]+39*a[n-2]$ makelist(a[n], n, 0, 17);
%o A190441 (Magma)  [n le 2 select n-1 else 4*Self(n-1)+39*Self(n-2): n in [1..22]];
%o A190441 (PARI) x='x+O('x^30); concat([0], Vec(x/(1-4*x-39*x^2))) \\ _G. C. Greubel_, Dec 30 2017
%Y A190441 Cf. A015611, A190943 (with similar closed forms).
%K A190441 nonn,easy
%O A190441 0,3
%A A190441 _Bruno Berselli_, May 25 2011