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%I #46 Dec 24 2023 09:37:26
%S 0,6,60,594,5880,58206,576180,5703594,56459760,558894006,5532480300,
%T 54765908994,542126609640,5366500187406,53122875264420,
%U 525862252456794,5205499649303520,51529134240578406,510085842756480540,5049329293324226994,49983207090485789400
%N a(n) = 10*a(n-1) - a(n-2) with a(0)=0, a(1)=6.
%C Kekulé numbers for the benzenoids P''(n).
%C 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
%C Numbers n such that 6*n^2 + 9 is a square. - _Colin Barker_, Mar 17 2014
%D S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 301).
%H Harvey P. Dale, <a href="/A122653/b122653.txt">Table of n, a(n) for n = 0..1000</a>
%H Hacène Belbachir, Soumeya Merwa Tebtoub, and László Németh, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL23/Nemeth/nemeth7.html">Ellipse Chains and Associated Sequences</a>, J. Int. Seq., Vol. 23 (2020), Article 20.8.5.
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-1).
%F G.f.: 6x/(1 - 10x + x^2). - _Philippe Deléham_, Nov 17 2008
%F a(n) = 6*A004189(n). - _R. J. Mathar_, Jun 22 2020
%F 6*a(n)^2+9 = (3*A001079(n))^2 - detail of the Barker comment. - _R. J. Mathar_, Jun 22 2020
%t CoefficientList[Series[(6 z)/(z^2 - 10 z + 1), {z, 0, 200}], z] (* _Vladimir Joseph Stephan Orlovsky_, Jun 11 2011 *)
%t LinearRecurrence[{10,-1},{0,6},30] (* _Harvey P. Dale_, Dec 16 2014 *)
%o (PARI) a(n)=if(n<2,(n%2)*6,10*a(n-1)-a(n-2)) \\ _Benoit Cloitre_, Sep 23 2006
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Sep 21 2006
%E More terms and better definition from _Benoit Cloitre_, Sep 23 2006
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