login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A057198 a(n) = (5*3^(n-1)+1)/2. 9
3, 8, 23, 68, 203, 608, 1823, 5468, 16403, 49208, 147623, 442868, 1328603, 3985808, 11957423, 35872268, 107616803, 322850408, 968551223, 2905653668, 8716961003, 26150883008, 78452649023, 235357947068, 706073841203, 2118221523608 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

It appears that if s(n) is a first order rational sequence of the form s(0)=4, s(n)= (2*s(n-1)+1)/(s(n-1)+2), n>0, then s(n) = a(n)/(a(n)-1), n>0.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Nathan Fox, A Slow Relative of Hofstadter's Q-Sequence, arXiv:1611.08244 [math.NT], 2016.

Index entries for linear recurrences with constant coefficients, signature (4,-3).

FORMULA

a(n+1) = 3*a(n) - 1 for n > 1. [Reinhard Zumkeller, Jan 22 2011]

G.f.: 5/2*U(0) where U(k)=  1 + 2/(5*3^k + 5*3^k/(1 - 30*x*3^k/(15*x*3^k - 1/U(k+1)))) ; (continued fraction, 4-step). - Sergei N. Gladkovskii, Nov 01 2012

E.g.f.: 5/2*U(0) where U(k)=  1 + 2/(5*3^k + 5*3^k/(1 - 30*x*3^k/(15*x*3^k - (k+1)/U(k+1)))) ; (continued fraction, 4-step). - Sergei N. Gladkovskii, Nov 01 2012

G.f.: -x*(-3+4*x) / ( (3*x-1)*(x-1) ). - R. J. Mathar, Jan 25 2015

EXAMPLE

G.f. = 3*x + 8*x^2 + 23*x^3 + 68*x^4 + 203*x^5 + 608*x^6 + 1823*x^7 + 5468*x^8 + ...

MATHEMATICA

Table[(5*3^(n-1) + 1)/2, {n, 30}] (* T. D. Noe, Oct 11 2012 *)

PROG

(PARI) a(n)=(5*3^(n-1)+1)/2 \\ Charles R Greathouse IV, Oct 11 2012

(MAGMA) [(5*3^(n-1) + 1)/2: n in [1..30]]; // Vincenzo Librandi, Oct 11 2012

CROSSREFS

Related to A046901.

Equals A060816 + 1.

Sequence in context: A038151 A230122 A199103 * A025262 A056010 A002712

Adjacent sequences:  A057195 A057196 A057197 * A057199 A057200 A057201

KEYWORD

nonn,easy

AUTHOR

Colin Mallows and N. J. A. Sloane, Sep 16 2000

EXTENSIONS

Incorrect zero-th term removed by Jon Perry, Oct 11 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 19 02:01 EST 2018. Contains 317332 sequences. (Running on oeis4.)