cp's OEIS Frontend

A164021 a(n) = 12*a(n-1) - 34*a(n-2) for n > 1; a(0) = 3, a(1) = 22.

%I A164021 #11 Sep 08 2022 08:45:47
%S A164021 3,22,162,1196,8844,65464,484872,3592688,26626608,197367904,
%T A164021 1463110176,10846813376,80416014528,596200519552,4420261740672,
%U A164021 32772323223296,242978979496704,1801488764368384,13356579869532672,99028340445867008
%N A164021 a(n) = 12*a(n-1) - 34*a(n-2) for n > 1; a(0) = 3, a(1) = 22.
%C A164021 Binomial transform of A163605.
%H A164021 G. C. Greubel, <a href="/A164021/b164021.txt">Table of n, a(n) for n = 0..1000</a>
%H A164021 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (12, -34).
%F A164021 a(n) = ((3+2*sqrt(2))*(6+sqrt(2))^n+(3-2*sqrt(2))*(6-sqrt(2))^n)/2.
%F A164021 G.f.: (3-14*x)/(1-12*x+34*x^2).
%F A164021 E.g.f.: (3*cosh(sqrt(2)*x) + 2*sqrt(2)*sinh(sqrt(2)*x))*exp(6*x). - _G. C. Greubel_, Sep 07 2017
%t A164021 LinearRecurrence[{12,-34},{3,22},20] (* _Harvey P. Dale_, Oct 19 2012 *)
%o A164021 (Magma) [ n le 2 select 19*n-16 else 12*Self(n-1)-34*Self(n-2): n in [1..20] ];
%o A164021 (PARI) x='x+O('x^50); Vec((3-14*x)/(1-12*x+34*x^2)) \\ _G. C. Greubel_, Sep 07 2017
%Y A164021 Cf. A163605.
%K A164021 nonn
%O A164021 0,1
%A A164021 _Klaus Brockhaus_, Aug 08 2009