The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A057198 a(n) = (5*3^(n-1)+1)/2. 12
 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. Cf. A135423 (bisection), A191450 (2nd row). 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 zeroth 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 30 12:16 EDT 2022. Contains 354939 sequences. (Running on oeis4.)