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A123358 Kekulé numbers for certain benzenoids (see the Cyvin-Gutman book for details).

%I A123358 #16 Apr 03 2020 07:53:00
%S A123358 1,10,125,1625,21250,278125,3640625,47656250,623828125,8166015625,
%T A123358 106894531250,1399267578125,18316650390625,239768066406250,
%U A123358 3138604736328125,41084869384765625,537807922363281250,7039997100830078125,92154758453369140625,1206321449279785156250,15790952777862548828125,206706255435943603515625
%N A123358 Kekulé numbers for certain benzenoids (see the Cyvin-Gutman book for details).
%H A123358 S. J. Cyvin and I. Gutman, <a href="https://doi.org/10.1007/978-3-662-00892-8_12">Kekulé structures in benzenoid hydrocarbons</a>, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (see p. 210, formula page 204).
%H A123358 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (15,-25).
%F A123358 G.f.: -(5*x-1) / (25*x^2-15*x+1). - _Colin Barker_, Aug 29 2013
%F A123358 a(n) = 5^n*A001519(n+1). - _R. J. Mathar_, Jul 26 2019
%p A123358 A123358 := proc(n)
%p A123358     option remember;
%p A123358     if n <= 1 then
%p A123358         op(n+1,[1,10]) ;
%p A123358     else
%p A123358         15*procname(n-1)-25*procname(n-2) ;
%p A123358     end if
%p A123358 end proc:
%p A123358 seq( A123358(n),n=0..30) ; # _R. J. Mathar_, Jul 26 2019
%t A123358 LinearRecurrence[{15, -25}, {1, 10}, 30] (* _Jean-François Alcover_, Apr 03 2020 *)
%Y A123358 Cf. A001519.
%K A123358 nonn,easy
%O A123358 0,2
%A A123358 _N. J. A. Sloane_, Oct 10 2006