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A164311 a(n) = 12*a(n-1) - 33*a(n-2) for n > 1; a(0) = 4, a(1) = 27.

%I A164311 #9 Sep 08 2022 08:45:47
%S A164311 4,27,192,1413,10620,80811,619272,4764501,36738036,283627899,
%T A164311 2191179600,16934434533,130904287596,1012015111563,7824339848088,
%U A164311 60495579495477,467743738958820,3616570744155099,27963305544220128,216212831973523269
%N A164311 a(n) = 12*a(n-1) - 33*a(n-2) for n > 1; a(0) = 4, a(1) = 27.
%C A164311 Binomial transform of A162561. Sixth binomial transform of A162766.
%H A164311 G. C. Greubel, <a href="/A164311/b164311.txt">Table of n, a(n) for n = 0..1000</a>
%H A164311 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (12,-33).
%F A164311 a(n) = ((4+sqrt(3))*(6+sqrt(3))^n + (4-sqrt(3))*(6-sqrt(3))^n)/2.
%F A164311 G.f.: (4-21*x)/(1-12*x+33*x^2).
%F A164311 E.g.f.: (4*cosh(sqrt(3)*x) + sqrt(3)*sinh(sqrt(3)*x))*exp(6*x). - _G. C. Greubel_, Sep 13 2017
%t A164311 LinearRecurrence[{12,-33}, {4,27}, 50] (* or *) CoefficientList[Series[(4 - 21*x)/(1 - 12*x + 33*x^2), {x,0,50}], x] (* _G. C. Greubel_, Sep 13 2017 *)
%o A164311 (Magma) [ n le 2 select 23*n-19 else 12*Self(n-1)-33*Self(n-2): n in [1..20] ];
%o A164311 (PARI) x='x+O('x^50); Vec((4-21*x)/(1-12*x+33*x^2)) \\ _G. C. Greubel_, Sep 13 2017
%Y A164311 Cf. A162561, A162766.
%K A164311 nonn,easy
%O A164311 0,1
%A A164311 _Klaus Brockhaus_, Aug 12 2009