A163472 - OEIS

%I #11 Sep 08 2022 08:45:46

%S 3,21,153,1143,8667,66285,509409,3925503,30295539,234004869,

%T 1808305641,13977507015,108055998027,835414244829,6459123003057,

%U 49940805957327,386138612387043,2985616752052725,23084826815860281,178492568972583447

%N a(n) = 12*a(n-1) - 33*a(n-2) for n > 1; a(0) = 3, a(1) = 21.

%C Binomial transform of A163471. Inverse binomial transform of A163473.

%H G. C. Greubel, <a href="/A163472/b163472.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,-33).

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

%F G.f.: (3-15*x)/(1-12*x+33*x^2).

%F E.g.f.: exp(6*x)*( 3*cosh(sqrt(3)*x) + sqrt(3)*sinh(sqrt(3)*x) ). - _G. C. Greubel_, Jul 26 2017

%t LinearRecurrence[{12, -33}, {3, 21}, 50] (* _G. C. Greubel_, Jul 26 2017 *)

%o (Magma) [ n le 2 select 18*n-15 else 12*Self(n-1)-33*Self(n-2): n in [1..20] ];

%o (PARI) x='x+O('x^50); Vec((3-15*x)/(1-12*x+33*x^2)) \\ _G. C. Greubel_, Jul 26 2017

%Y Cf. A163471, A163473.

%K nonn

%O 0,1

%A _Klaus Brockhaus_, Aug 11 2009