%I A161727
%S A161727 1,6,35,202,1161,6662,38203,219018,1255505,7196806,41252883,236464586,
%T A161727 1355429209,7769394054,44534572715,255274459018,1463246226849,
%U A161727 8387401847558,48077013831427,275579886633162,1579637913256745
%N A161727 a(n) = ((2+sqrt(3))*(4+sqrt(3))^n-(2-sqrt(3))*(4-sqrt(3))^n)/sqrt(12).
%C A161727 Fourth binomial transform of A133626, binomial transform of A140766.
%F A161727 a(n) = 8*a(n-1)-13(n-2) for n > 1; a(0) = 1, a(1) = 6.
%F A161727 G.f.: (1-2*x)/(1-8*x+13*x^2). [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), 
               Jun 19 2009]
%p A161727 seq(expand(((2+sqrt(3))*(4+sqrt(3))^n-(2-sqrt(3))*(4-sqrt(3))^n)/sqrt(12)), 
               n = 0 .. 20); [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 
               20 2009]
%o A161727 (PARI) {default(debug, 0); F=nfinit(x^2-3); for(n=0, 20, print1(nfeltdiv(F, 
               ((2+x)*(4+x)^n-(2-x)*(4-x)^n), (2*x))[1], ","))} [From Klaus Brockhaus 
               (klaus-brockhaus(AT)t-online.de), Jun 19 2009]
%Y A161727 Cf. A133626, A140766.
%Y A161727 Sequence in context: A131435 A079027 A081105 this_sequence A121838 A001109 
               A144638
%Y A161727 Adjacent sequences: A161724 A161725 A161726 this_sequence A161728 A161729 
               A161730
%K A161727 nonn
%O A161727 0,2
%A A161727 Al Hakanson (hawkuu(AT)gmail.com), Jun 17 2009
%E A161727 Extended beyond a(6) by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de) 
               and Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 19 2009
%E A161727 Edited by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jul 05 2009