A096053 a(n) = (3*9^n - 1)/2.
1, 13, 121, 1093, 9841, 88573, 797161, 7174453, 64570081, 581130733, 5230176601, 47071589413, 423644304721, 3812798742493, 34315188682441, 308836698141973, 2779530283277761, 25015772549499853, 225141952945498681
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
[(3*9^n-1)/2: n in [0..20]]; // Vincenzo Librandi, Nov 01 2011
-
Mathematica
Table[(3*9^n - 1)/2, {n, 0, 18}] (* L. Edson Jeffery, Feb 13 2015 *) -
PARI
a(n)=(3*9^n-1)/2 \\ Charles R Greathouse IV, Sep 28 2015
-
PARI
vector(30, n, n--; sigma(9^n)) \\ Altug Alkan, Nov 10 2015
Formula
From Paul Barry, May 27 2005: (Start)
G.f.: (1+3*x)/(1-10*x+9*x^2);
a(n) = Sum_{k=0..n} binomial(2n+1, 2k)*4^k;
a(n) = ((1+sqrt(4))*(5+2*sqrt(4))^n+(1-sqrt(4))*(5-2*sqrt(4))^n)/2. (End)
a(n-1) = (-9^n/3)*B(2n,1/3)/B(2n) where B(n,x) is the n-th Bernoulli polynomial and B(k)=B(k,0) is the k-th Bernoulli number.
a(n) = 10*a(n-1) - 9*a(n-2).
a(n) = 9*a(n-1) + 4. - Vincenzo Librandi, Nov 01 2011
a(n) = A320030(3^n-1). - Nathan M Epstein, Jan 02 2019
Extensions
Edited by N. J. A. Sloane, at the suggestion of Andrew S. Plewe, Jun 15 2007
Comments