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

0,1

Comments

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

Links

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).

Formula

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

Maple

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

Mathematica

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 *)

Prog

(Magma) [3^n+2: n in [0..30]];
(PARI) a(n)=3^n+2 \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

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).

Sequence in context: A279674 A194563 A080443 * A057735 A095302 A335367

Adjacent sequences: A168604 A168605 A168606 * A168608 A168609 A168610

Keyword

nonn,easy

Author

Vincenzo Librandi, Dec 01 2009

Extensions

Edited by Klaus Brockhaus, Apr 13 2010

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

Status

approved