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A162757 a(n) = 12*a(n-1)-33*a(n-2) for n > 1; a(0) = 1, a(1) = 7.

%I A162757 #5 Jun 30 2023 00:53:09
%S A162757 1,7,51,381,2889,22095,169803,1308501,10098513,78001623,602768547,
%T A162757 4659169005,36018666009,278471414943,2153041001019,16646935319109,
%U A162757 128712870795681,995205584017575,7694942271953427,59497522990861149
%N A162757 a(n) = 12*a(n-1)-33*a(n-2) for n > 1; a(0) = 1, a(1) = 7.
%C A162757 Sixth binomial transform of A108411. Binomial transform of A162558. Inverse binomial transform of A162758.
%H A162757 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (12, -33).
%F A162757 a(n) = ((3+sqrt(3))*(6+sqrt(3))^n+(3-sqrt(3))*(6-sqrt(3))^n)/6.
%F A162757 G.f.: (1-5*x)/(1-12*x+33*x^2).
%o A162757 (Magma) [ n le 2 select 6*n-5 else 12*Self(n-1)-33*Self(n-2): n in [1..20] ];
%Y A162757 Cf. A108411 (powers of 3 repeated), A162558, A162758.
%K A162757 nonn
%O A162757 0,2
%A A162757 _Klaus Brockhaus_, Jul 13 2009