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 A109113 a(n) = 6a(n-1) + 3a(n-2), a(0)=2, a(1)=14. 0

%I

%S 2,14,90,582,3762,24318,157194,1016118,6568290,42458094,274453434,

%T 1774094886,11467929618,74129862366,479182963050,3097487365398,

%U 20022473081538,129427300585422,836631222757146,5408069238299142

%N a(n) = 6a(n-1) + 3a(n-2), a(0)=2, a(1)=14.

%C KekulĂ© numbers for certain benzenoids.

%D S. J. Cyvin and I. Gutman, KekulĂ© structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 302, P_{15}).

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,3).

%F a(n) = ((3 + 2*sqrt(3))^(n+1) + (3 - 2*sqrt(3))^(n+1))/3.

%F G.f.: 2(1+z)/(1 - 6z - 3z^2).

%F a(n) = 2*abs(A099842(n)). - _F. Chapoton_, May 06 2014

%p a[0]:=2: a[1]:=14: for n from 2 to 25 do a[n]:=6*a[n-1]+3*a[n-2] od: seq(a[n],n=0..22);

%o (PARI) Vec((14+6*x)/(1-6*x-3*x^2)+O(x^99)) \\ _Charles R Greathouse IV_, May 06 2014

%Y Cf. A099842.

%K nonn,easy

%O 0,1

%A _Emeric Deutsch_, Jun 19 2005

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Last modified June 2 10:43 EDT 2020. Contains 334770 sequences. (Running on oeis4.)