A168609 -id:A168609 - cp's OEIS frontend

A168607 a(n) = 3^n + 2.

3, 5, 11, 29, 83, 245, 731, 2189, 6563, 19685, 59051, 177149, 531443, 1594325, 4782971, 14348909, 43046723, 129140165, 387420491, 1162261469, 3486784403, 10460353205, 31381059611, 94143178829, 282429536483, 847288609445

Offset: 0

Vincenzo Librandi, Dec 01 2009

Second bisection is A134752.
It appears that if s(n) is a first order rational sequence of the form s(1)=5, s(n)= (2*s(n-1)+1)/(s(n-1)+2),n>1, then s(n)= a(n)/(a(n)-4), n>1. - Gary Detlefs, Nov 16 2010
Mahler exhibits this sequence with n>=1 as a proof that there exists an infinite number of x coprime to 3, such that x belongs to A125293 and x^2 belongs to A005836. - Michel Marcus, Nov 12 2012

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Gennady Eremin, Arithmetization of well-formed parenthesis strings. Motzkin Numbers of the Second Kind, arXiv:2012.12675 [math.CO], 2020.
Kurt Mahler, The representation of squares to the base 3, Acta Arith. Vol. 53, Issue 1 (1989), p. 99-106.
Index entries for linear recurrences with constant coefficients, signature (4,-3).

Cf. A008776 (2*3^n), A005051 (8*3^n), A034472 (3^n+1), A000244 (powers of 3), A024023 (3^n-1), A168609 (3^n+4), A168610 (3^n+5), A134752 (3^(2*n-1)+2).

Magma
```
[3^n+2: n in [0..30]];
```

A168607:=n->3^n + 2; seq(A168607(n), n=0..30); # Wesley Ivan Hurt, Mar 21 2014

CoefficientList[Series[(3 - 7 x)/((1-x) (1-3 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Feb 06 2013 *)
NestList[3 # - 4 & , 3, 25] (* Bruno Berselli, Feb 06 2013 *)

a(n)=3^n+2 \\ Charles R Greathouse IV, Oct 07 2015

a(n) = 3*a(n-1) - 4, a(0) = 3.
a(n+1) - a(n) = A008776(n).
a(n+2) - a(n) = A005051(n).
a(n) = A034472(n)+1 = A000244(n)+2 = A024023(n)+3 = A168609(n)-2 = A168610(n)-3.
G.f.: (3 - 7*x)/((1 - x)*(1 - 3*x)).
a(n) = 4*a(n-1) - 3*a(n-2), a(0) = 3, a(1) = 5. - Vincenzo Librandi, Feb 06 2013
E.g.f.: exp(3*x) + 2*exp(x). - Elmo R. Oliveira, Nov 09 2023

Edited by Klaus Brockhaus, Apr 13 2010

Further edited by N. J. A. Sloane, Aug 10 2010

A178674 a(n) = 3^n + 3.

Original entry on oeis.org

4, 6, 12, 30, 84, 246, 732, 2190, 6564, 19686, 59052, 177150, 531444, 1594326, 4782972, 14348910, 43046724, 129140166, 387420492, 1162261470, 3486784404, 10460353206, 31381059612, 94143178830, 282429536484, 847288609446, 2541865828332, 7625597484990, 22876792454964

Offset: 0

Vincenzo Librandi, Dec 25 2010

a(n) is the deficiency of 3^n * 5. - Patrick J. McNab, May 27 2017

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-3).

Cf. A034472, A115098, A168607, A168609, A168610.

List([0..40], n -> 3^n+3); # G. C. Greubel, Jan 27 2019

Magma
```
[3^n+3: n in [0..35]];
```

Table[3^n+3, {n, 0, 40}] (* or *) CoefficientList[Series[(4-10x)/((1-x) (1-3x)), {x, 0, 30}], x] (* Vincenzo Librandi, May 13 2014 *)

a(n)=3^n+3 \\ Charles R Greathouse IV, Oct 07 2015

[3^n+3 for n in range(40)] # G. C. Greubel, Jan 27 2019

a(n) = 3*(a(n-1) - 2), a(0)=4.
From R. J. Mathar, Jan 05 2011: (Start)
G.f.: (4-10*x)/((1-3*x)*(1-x)).
a(n) = 2*A115098(n). (End)
a(n) = 4*a(n-1) - 3*a(n-2) for n > 1. - Vincenzo Librandi, May 13 2014
E.g.f.: exp(x)*(exp(2*x) + 3). - Elmo R. Oliveira, Apr 02 2025

cp's OEIS Frontend

A168607 a(n) = 3^n + 2.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

Formula

Extensions