A092167 Let M = 2 X 2 matrix [ 1 2 / 5 4 ]; a(n) = (2,2) entry of M^n.

4, 26, 154, 926, 5554, 33326, 199954, 1199726, 7198354, 43190126, 259140754, 1554844526, 9329067154, 55974402926, 335846417554, 2015078505326, 12090471031954, 72542826191726, 435256957150354, 2611541742902126

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, A092165, A092166.

Programs

Mathematica

Table[ MatrixPower[{{1, 2}, {5, 4}}, n][[2, 2]], {n, 20}] (* Robert G. Wilson v, Apr 22 2004 *)

Formula

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

A092166 -(-1)^n.

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

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

G.f.: 2*x*(2+3*x)/((1+x)*(1-6*x)). (End)

Extensions

Edited by Robert G. Wilson v, Apr 22 2004