A140780 a(n) = 10*a(n-1) - a(n-2) for n >= 2 with a(0) = 1 and a(1) = 3.

1, 3, 29, 287, 2841, 28123, 278389, 2755767, 27279281, 270037043, 2673091149, 26460874447, 261935653321, 2592895658763, 25667020934309, 254077313684327, 2515106115908961, 24896983845405283, 246454732338143869, 2439650339536033407, 24150048663022190201

Offset

0,2

Comments

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

Term (1,1) in A^n where A = the 2 X 2 matrix [3,4; 5,7].

G.f.: (1-7*x)/(x^2-10*x+1). - Harvey P. Dale, Jan 19 2012

Example

a(3) = 287 = 10*a(2) - a(1) = 10*29 - 3.
a(3) = 287 = term (1,1) in A^3.

Mathematica

LinearRecurrence[{10, -1}, {1, 3}, 30] (* Harvey P. Dale, Jan 19 2012 *)

Crossrefs

Sequence in context: A026130 A026159 A025186 * A268493 A002669 A340990

Adjacent sequences: A140777 A140778 A140779 * A140781 A140782 A140783

Keyword

nonn

Author

Gary W. Adamson, May 30 2008

Extensions

More terms from Harvey P. Dale, Jan 19 2012

Status

approved