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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A156156 a(n) = 6*a(n-1)-a(n-2) for n > 2; a(1) = 13, a(2) = 53. 4
 13, 53, 305, 1777, 10357, 60365, 351833, 2050633, 11951965, 69661157, 406014977, 2366428705, 13792557253, 80388914813, 468540931625, 2730856674937, 15916599117997, 92768738033045, 540695829080273, 3151406236448593 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS lim_{n -> infinity} a(n)/a(n-1) = 3+2*sqrt(2). LINKS Table of n, a(n) for n=1..20. Index entries for linear recurrences with constant coefficients, signature (6, -1). FORMULA a(n) = ((50+31*sqrt(2))*(3-2*sqrt(2))^n+(50-31*sqrt(2))*(3+2*sqrt(2))^n)/4. G.f.: x*(13-25*x)/(1-6*x+x^2). PROG (PARI) {m=20; v=concat([13, 53], vector(m-2)); for(n=3, m, v[n]=6*v[n-1]-v[n-2]); v} CROSSREFS First trisection of A155923. Cf. A156035 (decimal expansion of 3+2*sqrt(2)), A156157, A156158. Sequence in context: A142188 A248409 A206444 * A201486 A176617 A254895 Adjacent sequences: A156153 A156154 A156155 * A156157 A156158 A156159 KEYWORD nonn AUTHOR Klaus Brockhaus, Feb 09 2009 EXTENSIONS Replaced abbreviation by sqrt(2) Klaus Brockhaus, Feb 12 2009 G.f. corrected by Klaus Brockhaus, Sep 23 2009 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 July 24 12:16 EDT 2024. Contains 374583 sequences. (Running on oeis4.)