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A163472 a(n) = 12*a(n-1) - 33*a(n-2) for n > 1; a(0) = 3, a(1) = 21.

%I A163472 #11 Sep 08 2022 08:45:46
%S A163472 3,21,153,1143,8667,66285,509409,3925503,30295539,234004869,
%T A163472 1808305641,13977507015,108055998027,835414244829,6459123003057,
%U A163472 49940805957327,386138612387043,2985616752052725,23084826815860281,178492568972583447
%N A163472 a(n) = 12*a(n-1) - 33*a(n-2) for n > 1; a(0) = 3, a(1) = 21.
%C A163472 Binomial transform of A163471. Inverse binomial transform of A163473.
%H A163472 G. C. Greubel, <a href="/A163472/b163472.txt">Table of n, a(n) for n = 0..1000</a>
%H A163472 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (12,-33).
%F A163472 a(n) = ((3+sqrt(3))*(6+sqrt(3))^n + (3-sqrt(3))*(6-sqrt(3))^n)/2.
%F A163472 G.f.: (3-15*x)/(1-12*x+33*x^2).
%F A163472 E.g.f.: exp(6*x)*( 3*cosh(sqrt(3)*x) + sqrt(3)*sinh(sqrt(3)*x) ). - _G. C. Greubel_, Jul 26 2017
%t A163472 LinearRecurrence[{12, -33}, {3, 21}, 50] (* _G. C. Greubel_, Jul 26 2017 *)
%o A163472 (Magma) [ n le 2 select 18*n-15 else 12*Self(n-1)-33*Self(n-2): n in [1..20] ];
%o A163472 (PARI) x='x+O('x^50); Vec((3-15*x)/(1-12*x+33*x^2)) \\ _G. C. Greubel_, Jul 26 2017
%Y A163472 Cf. A163471, A163473.
%K A163472 nonn
%O A163472 0,1
%A A163472 _Klaus Brockhaus_, Aug 11 2009