A163471 - OEIS

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

%S 3,18,114,744,4932,32952,221016,1485216,9989808,67223328,452457504,

%T 3045661824,20502553152,138020971392,929153544576,6255074075136,

%U 42109362770688,283481998053888,1908413999583744,12847536038651904

%N a(n) = 10*a(n-1) - 22*a(n-2) for n > 1; a(0) = 3, a(1) = 18.

%C Binomial transform of A163470. Inverse binomial transform of A163472.

%H G. C. Greubel, <a href="/A163471/b163471.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 (10,-22).

%F a(n) = ((3+sqrt(3))*(5+sqrt(3))^n + (3-sqrt(3))*(5-sqrt(3))^n)/2.

%F G.f.: (3-12*x)/(1-10*x+22*x^2).

%F E.g.f.: exp(5*x)*( 3*cosh(sqrt(3)*x) + sqrt(3)*sinh(sqrt(3)*x) ). - _G. C. Greubel_, Jul 26 2017

%t LinearRecurrence[{10, -22}, {3, 18}, 50] (* _G. C. Greubel_, Jul 26 2017 *)

%o (Magma) [ n le 2 select 15*n-12 else 10*Self(n-1)-22*Self(n-2): n in [1..20] ];

%o (PARI) x='x+O('x^50); Vec((3-12*x)/(1-10*x+22*x^2)) \\ _G. C. Greubel_, Jul 26 2017

%Y Cf. A163470, A163472.

%K nonn

%O 0,1

%A _Klaus Brockhaus_, Aug 11 2009