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