A163066 - OEIS

%I #7 Sep 08 2022 08:45:46

%S 2,17,142,1177,9722,80177,660742,5443417,44838002,369310097,

%T 3041743102,25052304217,206333614442,1699381942577,13996241263222,

%U 115274054938777,949405180105442,7819366458163217,64400836914689902,530409682773219097

%N a(n) = 12*a(n-1) - 31*a(n-2) for n > 1; a(0) = 2, a(1) = 17.

%C Binomial transform of A162773. Inverse binomial transform of A163067.

%H G. C. Greubel, <a href="/A163066/b163066.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,-31).

%F a(n) = ((2+sqrt(5))*(6+sqrt(5))^n + (2-sqrt(5))*(6-sqrt(5))^n)/2.

%F G.f.: (2-7*x)/(1-12*x+31*x^2).

%t CoefficientList[Series[(2-7*x)/(1-12*x+31*x^2), {x,0,50}],x] (* or *) LinearRecurrence[{12,-31}, {2,17}, 30] (* _G. C. Greubel_, Dec 22 2017 *)

%o (Magma) [ n le 2 select 15*n-13 else 12*Self(n-1)-31*Self(n-2): n in [1..20] ];

%o (PARI) x='x+O('x^30); Vec((2-7*x)/(1-12*x+31*x^2)) \\ _G. C. Greubel_, Dec 22 2017

%Y Cf. A162773, A163067.

%K nonn

%O 0,1

%A _Klaus Brockhaus_, Jul 20 2009