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a(n) = 14*a(n-1) - 44*a(n-2) for n > 1; a(0) = 2, a(1) = 19.
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%I #7 Sep 08 2022 08:45:46

%S 2,19,178,1656,15352,142064,1313408,12136896,112126592,1035748864,

%T 9566914048,88363846656,816149635072,7538085638144,69622614990848,

%U 643040841793536,5939176725512192,54854677118255104,506641703733035008

%N a(n) = 14*a(n-1) - 44*a(n-2) for n > 1; a(0) = 2, a(1) = 19.

%C Binomial transform of A163066. Inverse binomial transform of A163068.

%H G. C. Greubel, <a href="/A163067/b163067.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 (14,-44).

%F a(n) = ((2+sqrt(5))*(7+sqrt(5))^n+(2-sqrt(5))*(7-sqrt(5))^n)/2.

%F G.f.: (2-9*x)/(1-14*x+44*x^2).

%t CoefficientList[Series[(2-9*x)/(1-14*x+44*x^2), {x,0,50}],x] (* or *) LinearRecurrence[{14,-44}, {2,19}, 30] (* _G. C. Greubel_, Dec 22 2017 *)

%o (Magma) [ n le 2 select 17*n-15 else 14*Self(n-1)-44*Self(n-2): n in [1..20] ];

%o (PARI) x='x+O('x^30); Vec((2-9*x)/(1-14*x+44*x^2)) \\ _G. C. Greubel_, Dec 22 2017

%Y Cf. A163066, A163068.

%K nonn

%O 0,1

%A _Klaus Brockhaus_, Jul 20 2009