A092165 Let M = 2 X 2 matrix [ 1 2 / 5 4 ]; a(n) = (1,2) entry of M^n.

2, 10, 62, 370, 2222, 13330, 79982, 479890, 2879342, 17276050, 103656302, 621937810, 3731626862, 22389761170, 134338567022, 806031402130, 4836188412782, 29017130476690, 174102782860142, 1044616697160850, 6267700182965102, 37606201097790610, 225637206586743662

Offset: 1

Author

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

Keywords

• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (5,6).

Crossrefs

Cf. A092164, A092166, A092167.

Programs

Magma

[(2*6^n - 2*(-1)^n)/7: n in [1..30]]; // Vincenzo Librandi, Jul 21 2015

Mathematica

Table[ MatrixPower[{{1, 2}, {5, 4}}, n][[1, 2]], {n, 20}] (* Robert G. Wilson v, Apr 22 2004 *)
LinearRecurrence[{5, 6}, {2, 10}, 25] (* Vincenzo Librandi, Jul 21 2015 *)

Formula

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

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

From R. J. Mathar, Apr 20 2009: (Start)

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

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

Extensions

Edited by Robert G. Wilson v, Apr 22 2004

More terms from Vincenzo Librandi, Jul 21 2015