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a(n) = 12*a(n-1) - 34*a(n-2) for n > 1; a(0) = 3, a(1) = 22.
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%I #11 Sep 08 2022 08:45:47

%S 3,22,162,1196,8844,65464,484872,3592688,26626608,197367904,

%T 1463110176,10846813376,80416014528,596200519552,4420261740672,

%U 32772323223296,242978979496704,1801488764368384,13356579869532672,99028340445867008

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

%C Binomial transform of A163605.

%H G. C. Greubel, <a href="/A164021/b164021.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 (12, -34).

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

%F G.f.: (3-14*x)/(1-12*x+34*x^2).

%F 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 LinearRecurrence[{12,-34},{3,22},20] (* _Harvey P. Dale_, Oct 19 2012 *)

%o (Magma) [ n le 2 select 19*n-16 else 12*Self(n-1)-34*Self(n-2): n in [1..20] ];

%o (PARI) x='x+O('x^50); Vec((3-14*x)/(1-12*x+34*x^2)) \\ _G. C. Greubel_, Sep 07 2017

%Y Cf. A163605.

%K nonn

%O 0,1

%A _Klaus Brockhaus_, Aug 08 2009