A135423 a(n) = (5*9^n + 1)/2.

3, 23, 203, 1823, 16403, 147623, 1328603, 11957423, 107616803, 968551223, 8716961003, 78452649023, 706073841203, 6354664570823, 57191981137403, 514727830236623, 4632550472129603, 41692954249166423, 375236588242497803

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (10,-9).

Formula

a(n) = 9*a(n-1) - 4 for n>0, a(0)=3.

O.g.f.: (1/(1-x) - 5/(9*x-1))/2. - R. J. Mathar, Feb 19 2008

a(n) = 10*a(n-1) - 9*a(n-2). - Vincenzo Librandi, Nov 08 2011

E.g.f.: (1/2)*( 5*exp(9*x) + exp(x) ). - G. C. Greubel, Oct 14 2016

Mathematica

Table[ (5*9^n + 1)/2, {n, 0, 25}] (* or *) LinearRecurrence[{10, -9}, {3, 23}, 25] (* G. C. Greubel, Oct 14 2016 *)

Prog

(Magma) [(5*9^n+1)/2: n in [0..30]]; // Vincenzo Librandi, Nov 08 2011

Crossrefs

Bisection of A057198. Cf. A191450.

Sequence in context: A370283 A235131 A235360 * A114017 A316085 A068691

Adjacent sequences: A135420 A135421 A135422 * A135424 A135425 A135426

Keyword

nonn,easy

Author

Paul Curtz, Feb 18 2008

Extensions

More terms from R. J. Mathar, Feb 19 2008

Definition rewritten (with Mathar's formula) from Bruno Berselli, Nov 08 2011

Status

approved