%I A140766
%S A140766 1,5,24,114,540,2556,12096,57240,270864,1281744,6065280,28701216,
%T A140766 135815616,642686400,3041224704,14391229824,68100030720,322252805376,
%U A140766 1524916647936,7215983055360
%N A140766 a(n) = 6*a(n-1) - 6*a(n-2).
%C A140766 Companion sequence = A030192 beginning (1, 6, 30, 144, 684,...).
%F A140766 a(n) = 6*a(n-1) - 6*a(n-2); given a(1) = 1, a(2) = 5. Term (1,1) of X^n, 
               where X = the 3x3 matrix [1,1,1; 1,2,1; 3,1,3].
%F A140766 O.g.f.: x(1-x)/(1-6x+6x^2). a(n)=A030192(n-1)-A030192(n-2). - R. J. Mathar 
               (mathar(AT)strw.leidenuniv.nl), May 31 2008
%F A140766 a(n)=(1/2)*[3-sqrt(3)]^n+(1/3)*sqrt(3)*[3+sqrt(3)]^n+(1/2)*[3+sqrt(3)]^n-(1/
               3)*[3-sqrt(3)]^n *sqrt(3), with n>=0 - Paolo P. Lava (ppl(AT)spl.at), 
               Jun 25 2008
%e A140766 a(5) = 540 = 6*a(4) - 6*a(3) = 6*(114) - 6*24.
%e A140766 a(5) = 540 = term (1,1) of X^5.
%Y A140766 Cf. A030192.
%Y A140766 Sequence in context: A081104 A079028 A141223 this_sequence A026388 A057969 
               A004254
%Y A140766 Adjacent sequences: A140763 A140764 A140765 this_sequence A140767 A140768 
               A140769
%K A140766 nonn
%O A140766 1,2
%A A140766 Gary W. Adamson & Roger L. Bagula (qntmpkt(AT)yahoo.com), May 28 2008
%E A140766 More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 31 2008