A140781 a(n) = 10*a(n-1) - a(n-2).

1, 2, 19, 188, 1861, 18422, 182359, 1805168, 17869321, 176888042, 1751011099, 17333222948, 171581218381, 1698478960862, 16813208390239, 166433604941528, 1647522841025041, 16308794805308882, 161440425212063779, 1598095457315328908, 15819514147941225301

Offset

0,2

Comments

A140780 has the same recursion rule but starts (1, 3, 29,...).

a(n)/a(n-1) tends to 2*sqrt(6) + 5 = 9.8989794855...

Links

Table of n, a(n) for n=0..20.

Index entries for linear recurrences with constant coefficients, signature (10, -1).

Formula

a(n) = 10*a(n-1) - a(n-2); n>1; given a(0) = 1, a(1) = 2. a(n) = term (1,1) in X^n, where X = the 2x2 matrix [2,3; 5,8].

Example

a(5) = 18422 = 10*a(4) - a(3) = 10*1861 - 188.
a(3) = 188 = term (1,1) of X^3.

Mathematica

LinearRecurrence[{10, -1}, {1, 2}, 30] (* Amiram Eldar, Dec 04 2018 *)

Crossrefs

Cf. A140780.

Sequence in context: A163067 A221904 A124262 * A128970 A218117 A145104

Adjacent sequences: A140778 A140779 A140780 * A140782 A140783 A140784

Keyword

nonn

Author

Gary W. Adamson, May 30 2008

Extensions

More terms from Amiram Eldar, Dec 04 2018

Status

approved