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%I #16 Apr 03 2020 07:52:53
%S 1,6,40,272,1856,12672,86528,590848,4034560,27549696,188121088,
%T 1284571136,8771600384,59896233984,408997068800,2792806678528,
%U 19070476877824,130221361594368,889207077732352,6071885729103872,41461429210972160,283116347854946304,1933239349151793152
%N Kekulé numbers for certain benzenoids (see the Cyvin-Gutman book for details).
%H 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 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-8).
%F G.f.: -(2*x-1) / (8*x^2-8*x+1). - _Colin Barker_, Aug 29 2013
%F a(n) = A057084(n)-2*A057084(n-1). - _R. J. Mathar_, Jul 26 2019
%p A123357 := proc(n)
%p option remember;
%p if n <= 1 then
%p op(n+1,[1,6]) ;
%p else
%p 8*(procname(n-1)-procname(n-2)) ;
%p end if
%p end proc:
%p seq( A123357(n),n=0..30) ; # _R. J. Mathar_, Jul 26 2019
%t LinearRecurrence[{8, -8}, {1, 6}, 30] (* _Jean-François Alcover_, Apr 03 2020 *)
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Oct 10 2006
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