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A092164 Let M = 2 X 2 matrix [ 1 2 / 5 4 ]; a(n) = (1,1) entry of M^n. 4

%I #7 Jul 21 2015 00:40:37

%S 1,11,61,371,2221,13331,79981,479891,2879341,17276051,103656301,

%T 621937811,3731626861,22389761171,134338567021,806031402131,

%U 4836188412781,29017130476691,174102782860141,1044616697160851

%N Let M = 2 X 2 matrix [ 1 2 / 5 4 ]; a(n) = (1,1) entry of M^n.

%F a(n) = (2*6^n + 5*(-1)^n)/7.

%F A092165 +(-1)^n.

%F a(n)=5*a(n-1)+6*a(n-2). G.f.: x*(1+6*x)/((1+x)*(1-6*x)). - _R. J. Mathar_, Apr 20 2009

%t Table[ MatrixPower[{{1, 2}, {5, 4}}, n][[1, 1]], {n, 20}] (* _Robert G. Wilson v_, Apr 22 2004 *)

%Y Cf. A092165, A092166, A092167.

%K nonn

%O 1,2

%A Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Apr 01 2004

%E Edited by _Robert G. Wilson v_, Apr 22 2004

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