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

1, 11, 61, 371, 2221, 13331, 79981, 479891, 2879341, 17276051, 103656301, 621937811, 3731626861, 22389761171, 134338567021, 806031402131, 4836188412781, 29017130476691, 174102782860141, 1044616697160851

Offset

1,2

Links

Table of n, a(n) for n=1..20.

Formula

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

A092165 +(-1)^n.

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

Mathematica

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

Crossrefs

Cf. A092165, A092166, A092167.

Sequence in context: A199414 A156095 A068846 * A354336 A088545 A259257

Adjacent sequences: A092161 A092162 A092163 * A092165 A092166 A092167

Keyword

nonn

Author

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

Extensions

Edited by Robert G. Wilson v, Apr 22 2004

Status

approved