cp's OEIS Frontend

A171371 a(n) = 6*a(n-1) + 8*a(n-2) with a(1) = 8, a(2) = 18.

%I A171371 #30 Sep 08 2022 08:45:49
%S A171371 8,18,172,1176,8432,60000,427456,3044736,21688064,154486272,
%T A171371 1100422144,7838423040,55833915392,397710876672,2832936583168,
%U A171371 20179306512384,143739331739648,1023870442536960,7293137309138944,51949787395129344,370043822843887616
%N A171371 a(n) = 6*a(n-1) + 8*a(n-2) with a(1) = 8, a(2) = 18.
%C A171371 Seen on a quiz.
%C A171371 The recurrence was supplied by _Zak Seidov_, Dec 07 2009.
%H A171371 Vincenzo Librandi, <a href="/A171371/b171371.txt">Table of n, a(n) for n = 1..200</a>
%H A171371 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,8).
%F A171371 G.f.: 2*x*(-4 + 15*x)/(-1 + 6*x + 8*x^2). - _V.J. Pohjola_, Dec 07 2009
%F A171371 a(n) = 8*A189800(n) - 30*A189800(n-1). - _R. J. Mathar_, Nov 17 2011
%F A171371 From _Franck Maminirina Ramaharo_, Nov 23 2018: (Start)
%F A171371 a(n) = ((77*sqrt(17) - 255)*(sqrt(17) + 3)^n - (77*sqrt(17) + 255)*(3 - sqrt(17))^n)/136.
%F A171371 E.g.f.: ((77*sqrt(17)*sinh(sqrt(17)*x) - 255*cosh(sqrt(17)*x))*exp(3*x) + 255)/68. (End)
%t A171371 a[1] = 8; a[2] = 18; a[n_] := a[n] = 6*a[n - 1] + 8*a[n - 2]; Array[a, 20] (* _Amiram Eldar_, Nov 23 2018 *)
%o A171371 (Magma) I:=[8,18]; [n le 2 select I[n] else 6*Self(n-1)+8*Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Nov 18 2011
%K A171371 nonn,easy
%O A171371 1,1
%A A171371 Anonymous, Dec 06 2009
%E A171371 More terms from _N. J. A. Sloane_, Dec 07 2009
%E A171371 G.f. and name adapted to the offset by _Bruno Berselli_, Apr 04 2011