A092166 Let M = 2 X 2 matrix [ 1 2 / 5 4 ]; a(n) = (2,1) entry of M^n.

5, 25, 155, 925, 5555, 33325, 199955, 1199725, 7198355, 43190125, 259140755, 1554844525, 9329067155, 55974402925, 335846417555, 2015078505325, 12090471031955, 72542826191725, 435256957150355, 2611541742902125

Offset: 1

Author

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

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A092164, A092165, A092167.

Programs

Mathematica

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

Formula

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

a(n) = A092167(n) +(-1)^n.

From Colin Barker, Nov 08 2012: (Start)

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

G.f.: -5*x/((x+1)*(6*x-1)). (End)

Extensions

Edited by Robert G. Wilson v, Apr 22 2004