A122653 a(n) = 10*a(n-1) - a(n-2) with a(0)=0, a(1)=6.

0, 6, 60, 594, 5880, 58206, 576180, 5703594, 56459760, 558894006, 5532480300, 54765908994, 542126609640, 5366500187406, 53122875264420, 525862252456794, 5205499649303520, 51529134240578406, 510085842756480540, 5049329293324226994, 49983207090485789400

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