A198965 a(n) = 7*9^n - 1.

6, 62, 566, 5102, 45926, 413342, 3720086, 33480782, 301327046, 2711943422, 24407490806, 219667417262, 1977006755366, 17793060798302, 160137547184726, 1441237924662542, 12971141321962886, 116740271897665982, 1050662447078993846, 9455962023710944622, 85103658213398501606

Offset: 0

Author

Vincenzo Librandi, Nov 01 2011

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients,signature (10,-9).

Crossrefs

Cf. A198964.

Programs

Magma

[7*9^n-1: n in [0..20]];

Mathematica

CoefficientList[Series[2 (3 + x)/(1 - 10 x + 9 x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Jan 03 2013 *)
NestList[9#+8&,6,20] (* or *) LinearRecurrence[{10,-9},{6,62},20] (* Harvey P. Dale, Feb 26 2015 *)

PARI

a(n)=7*9^n-1 \\ Charles R Greathouse IV, Jul 05 2024

Formula

a(n) = 9*a(n-1)+8.

a(n) = 10*a(n-1)-9*a(n-2), n>1.

G.f.: 2*(3 + x)/(1 - 10*x + 9*x^2). - Vincenzo Librandi, Jan 03 2013

From Elmo R. Oliveira, Aug 16 2024: (Start)

E.g.f.: exp(x)*(7*exp(8*x) - 1).

a(n) = 2*A198964(n). (End)