cp's OEIS Frontend

A197189 a(n) = 3*a(n-1) + 5*a(n-2), with a(0)=1, a(1)=2.

%I A197189 #25 Mar 29 2024 05:43:56
%S A197189 1,2,11,43,184,767,3221,13498,56599,237287,994856,4171003,17487289,
%T A197189 73316882,307387091,1288745683,5403172504,22653245927,94975600301,
%U A197189 398193030538,1669457093119,6999336432047,29345294761736,123032566445443,515824173145009,2162635351662242
%N A197189 a(n) = 3*a(n-1) + 5*a(n-2), with a(0)=1, a(1)=2.
%H A197189 Bruno Berselli, <a href="/A197189/b197189.txt">Table of n, a(n) for n = 0..1000</a>
%H A197189 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,5).
%F A197189 G.f.: (1-x)/(1-3*x-5*x^2).
%F A197189 a(n) = ((29+sqrt(29))*(3+sqrt(29))^n+(29-sqrt(29))*(3-sqrt(29))^n)/(58*2^n).
%F A197189 a(n) = A015523(n+1)-A015523(n).
%F A197189 G.f.: G(0)*(1-x)/(2-3*x), where G(k)= 1 + 1/(1 - x*(29*k-9)/(x*(29*k+20) - 6/G(k+1))); (continued fraction). - _Sergei N. Gladkovskii_, Jun 17 2013
%t A197189 a = {1, 2}; Do[AppendTo[a, 3 a[[-1]] + 5 a[[-2]]], {24}]; a (* _Bruno Berselli_, Dec 26 2012 *)
%o A197189 (PARI) v=vector(26); v[1]=1; v[2]=2; for(i=3, #v, v[i]=3*v[i-1]+5*v[i-2]); v
%o A197189 (Magma) [n le 2 select n else 3*Self(n-1)+5*Self(n-2): n in [1..26]];
%Y A197189 Cf. for type of recurrence: A015523, A072263, A072264, A152187, A179606 and also A180140.
%K A197189 nonn,easy
%O A197189 0,2
%A A197189 _Bruno Berselli_, Oct 11 2011