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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
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
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
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

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Last modified March 19 04:26 EDT 2024. Contains 370952 sequences. (Running on oeis4.)