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
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (10,-9).
Programs
-
Magma
[(5*9^n+1)/2: n in [0..30]]; // Vincenzo Librandi, Nov 08 2011
-
Mathematica
Table[ (5*9^n + 1)/2, {n,0,25}] (* or *) LinearRecurrence[{10, -9}, {3, 23}, 25] (* G. C. Greubel, Oct 14 2016 *)
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
Extensions
More terms from R. J. Mathar, Feb 19 2008
Definition rewritten (with Mathar's formula) from Bruno Berselli, Nov 08 2011