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A083695 a(n) = 2*a(n-1) + 5*a(n-2). 2

%I #14 Sep 08 2022 08:45:10

%S 0,3,6,27,84,303,1026,3567,12264,42363,146046,503907,1738044,5995623,

%T 20681466,71341047,246089424,848884083,2928215286,10100850987,

%U 34842778404,120189811743,414593515506,1430136089727,4933239756984,17017159962603,58700518710126

%N a(n) = 2*a(n-1) + 5*a(n-2).

%C A002533(n)/a(n) converges to sqrt(2/3).

%H Vincenzo Librandi, <a href="/A083695/b083695.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2, 5).

%F G.f.: 3x/(1-2x-5x^2).

%F a(n) = 3[(1+sqrt(6))^n-(1-sqrt(6))^n]/(2*sqrt(6)).

%F a(n) = 3*A002533(n-1) + a(n-1).

%F G.f.: 1/Q(0) -1, where Q(k) = 1 + 5*x^2 - (3*k+4)*x + x*(3*k+1 - 5*x)/Q(k+1); (continued fraction). - _Sergei N. Gladkovskii_, Oct 07 2013

%t CoefficientList[Series[3x/(1-2x-5x^2), {x, 0, 25}], x]

%t LinearRecurrence[{2, 5}, {0, 3}, 27] (* _Arkadiusz Wesolowski_, May 21 2013 *)

%o (Magma) I:=[0,3]; [n le 2 select I[n] else 2*Self(n-1)+5*Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Oct 07 2013

%K easy,nonn

%O 0,2

%A Mario Catalani (mario.catalani(AT)unito.it), May 03 2003

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Last modified March 2 04:27 EST 2024. Contains 370460 sequences. (Running on oeis4.)