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
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