%I A140184
%S A140184 1,14,60,360,1904,10528,57280,313472,1711872,9355776,51117056,279316480,
%T A140184 1526198272,8339333120,45566902272,248982306816
%N A140184 a(n) = 2*a(n-1) + 16*a(n-2) + 16*a(n-3).
%C A140184 a(n)/a(n-1) tends to (2*sqrt(3) + 2) = an eigenvalue of matrix X and 
               a root to the characteristic polynomial x^3 - 2x^2 - 16x - 16.
%F A140184 a(n) - 2*a(n-1) + 16*a(n-2) + 16*a(n-3); for n>3, given a(1) = 1, a(2) 
               = 14, a(3) = 60. Term (1,1) of X^n, where X = the 3x3 matrix [1,2,
               3; 2,0,2; 3,2,1].
%F A140184 a(n) = (2/3)*[2+2*sqrt(3)]^n*sqrt(3)+[2+2*sqrt(3)]^n+[2-2*sqrt(3)]^n-(-2)^n-(2/
               3)*sqrt(3) *[2-2*sqrt(3)]^n, with n>= 0 - Paolo P. Lava (ppl(AT)spl.at), 
               Jun 06 2008
%e A140184 a(5) = 1904 = 2*a(4) + 16*a(3) + 16*a(2) = 2*360 + 16*60 + 16*14.
%e A140184 a(4) = 360 since term (1,1) of X^4 = 360.
%Y A140184 Sequence in context: A063492 A051799 A164540 this_sequence A025415 A125849 
               A003695
%Y A140184 Adjacent sequences: A140181 A140182 A140183 this_sequence A140185 A140186 
               A140187
%K A140184 nonn
%O A140184 1,2
%A A140184 Gary W. Adamson (qntmpkt(AT)yahoo.com), May 11 2008