%I #9 Jun 13 2015 00:51:51

%S 4,9,20,45,101,227,510,1146,2575,5786,13001,29213,65641,147494,331416,

%T 744685,1673292,3759853,8448313,18983187,42654834,95844542,215360731,

%U 483911170,1087338529,2443227497,5489882353,12335653674,27717962204

%N a(n) = 2a(n-1) + a(n-2) - a(n-3); a(0)=4, a(1)=9, a(2)=20.

%C Kekulé numbers for certain benzenoids.

%D S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (pp. 286, 288, K{S(n)})

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-1)

%F G.f.: (4 + z - 2z^2)/(1 - 2z - z^2 + z^3).

%F a(n) = A052534(n+2). - _R. J. Mathar_, Feb 03 2014

%p a[0]:=4:a[1]:=9:a[2]:=20: for n from 3 to 32 do a[n]:=2*a[n-1]+a[n-2]-a[n-3] od: seq(a[n],n=0..32);

%K nonn,easy

%O 0,1

%A _Emeric Deutsch_, Jun 19 2005