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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A122653 a(n) = 10*a(n-1) - a(n-2) with a(0)=0, a(1)=6. 3
 0, 6, 60, 594, 5880, 58206, 576180, 5703594, 56459760, 558894006, 5532480300, 54765908994, 542126609640, 5366500187406, 53122875264420, 525862252456794, 5205499649303520, 51529134240578406, 510085842756480540, 5049329293324226994, 49983207090485789400 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Kekulé numbers for the benzenoids P''(n). a(n) are the integer square roots of A032528(m) - 1. A001079 gives the value of m where these roots occur. Also see A122652. - Richard R. Forberg, Aug 05 2013 Numbers n such that 6*n^2 + 9 is a square. - Colin Barker, Mar 17 2014 REFERENCES S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 301). LINKS Harvey P. Dale, Table of n, a(n) for n = 0..1000 Hacène Belbachir, Soumeya Merwa Tebtoub, and László Németh, Ellipse Chains and Associated Sequences, J. Int. Seq., Vol. 23 (2020), Article 20.8.5. Tanya Khovanova, Recursive Sequences Index entries for linear recurrences with constant coefficients, signature (10,-1). FORMULA G.f.: 6x/(1 - 10x + x^2). - Philippe Deléham, Nov 17 2008 a(n) = 6*A004189(n). - R. J. Mathar, Jun 22 2020 6*a(n)^2+9 = (3*A001079(n))^2 - detail of the Barker comment. - R. J. Mathar, Jun 22 2020 MATHEMATICA CoefficientList[Series[(6 z)/(z^2 - 10 z + 1), {z, 0, 200}], z] (* Vladimir Joseph Stephan Orlovsky, Jun 11 2011 *) LinearRecurrence[{10, -1}, {0, 6}, 30] (* Harvey P. Dale, Dec 16 2014 *) PROG (PARI) a(n)=if(n<2, (n%2)*6, 10*a(n-1)-a(n-2)) \\ Benoit Cloitre, Sep 23 2006 CROSSREFS Sequence in context: A091710 A054880 A186656 * A299869 A136943 A179200 Adjacent sequences: A122650 A122651 A122652 * A122654 A122655 A122656 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Sep 21 2006 EXTENSIONS More terms and better definition from Benoit Cloitre, Sep 23 2006 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 August 10 05:56 EDT 2024. Contains 375044 sequences. (Running on oeis4.)