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A164310 a(n) = 6*a(n-1) - 6*a(n-2) for n > 1; a(0) = 4, a(1) = 15.

%I A164310 #9 Sep 08 2022 08:45:47
%S A164310 4,15,66,306,1440,6804,32184,152280,720576,3409776,16135200,76352544,
%T A164310 361304064,1709709120,8090430336,38284327296,181163381760,
%U A164310 857274326784,4056665670144,19196348060160,90838094340096,429850477679616
%N A164310 a(n) = 6*a(n-1) - 6*a(n-2) for n > 1; a(0) = 4, a(1) = 15.
%C A164310 Binomial transform of A077236. Inverse binomial transform of A083882 without initial 1.
%H A164310 G. C. Greubel, <a href="/A164310/b164310.txt">Table of n, a(n) for n = 0..1000</a>
%H A164310 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,-6).
%F A164310 a(n) = ((4+sqrt(3))*(3+sqrt(3))^n + (4-sqrt(3))*(3-sqrt(3))^n)/2.
%F A164310 G.f.: (4-9*x)/(1-6*x+6*x^2).
%F A164310 E.g.f.: (4*cosh(sqrt(3)*x) + sqrt(3)*sinh(sqrt(3)*x))*exp(3*x). - _G. C. Greubel_, Sep 13 2017
%t A164310 LinearRecurrence[{6,-6}, {4,15}, 50] (* or *) CoefficientList[Series[(4 - 9*x)/(1 - 6*x + 6*x^2), {x,0,50}], x] (* _G. C. Greubel_, Sep 13 2017 *)
%o A164310 (Magma) [ n le 2 select 11*n-7 else 6*Self(n-1)-6*Self(n-2): n in [1..22] ];
%o A164310 (PARI) x='x+O('x^50); Vec((4-9*x)/(1-6*x+6*x^2)) \\ _G. C. Greubel_, Sep 13 2017
%Y A164310 Cf. A077236, A083882.
%K A164310 nonn,easy
%O A164310 0,1
%A A164310 _Klaus Brockhaus_, Aug 12 2009