A092165 - OEIS

%I #16 Sep 08 2022 08:45:13

%S 2,10,62,370,2222,13330,79982,479890,2879342,17276050,103656302,

%T 621937810,3731626862,22389761170,134338567022,806031402130,

%U 4836188412782,29017130476690,174102782860142,1044616697160850,6267700182965102,37606201097790610,225637206586743662

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

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,6).

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

%F a(n) = A092164(n) -(-1)^n.

%F From _R. J. Mathar_, Apr 20 2009: (Start)

%F a(n) = 5*a(n-1) + 6*a(n-2) = 2*A015540(n).

%F G.f.: 2*x/((1+x)*(1-6*x)). (End)

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

%t LinearRecurrence[{5, 6}, {2, 10}, 25] (* _Vincenzo Librandi_, Jul 21 2015 *)

%o (Magma) [(2*6^n - 2*(-1)^n)/7: n in [1..30]]; // _Vincenzo Librandi_, Jul 21 2015

%Y Cf. A092164, A092166, A092167.

%K nonn

%O 1,1

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

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

%E More terms from _Vincenzo Librandi_, Jul 21 2015