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LinearRecurrence[{8, -8}, {1, 6}, 30] (* Jean-François Alcover, Apr 03 2020 *)

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1, 6, 40, 272, 1856, 12672, 86528, 590848, 4034560, 27549696, 188121088, 1284571136, 8771600384, 59896233984, 408997068800, 2792806678528, 19070476877824, 130221361594368, 889207077732352, 6071885729103872, 41461429210972160, 283116347854946304, 1933239349151793152, 13200984010374774784, 90141957289783853056, 615527786235272626176

G.f.: -(2*x-1) / (8*x^2-8*x+1). - Colin Barker, Aug 29 2013a(n) = A057084(n)-2*A057084(n-1). - _R. J. Mathar_, Jul 26 20192013

a(n) = A057084(n)-2*A057084(n-1). - R. J. Mathar, Jul 26 2019

1, 6, 40, 272, 1856, 12672, 86528, 590848, 4034560, 27549696, 188121088, 1284571136, 8771600384, 59896233984, 408997068800, 2792806678528, 19070476877824, 130221361594368, 889207077732352, 6071885729103872, 41461429210972160, 283116347854946304, 1933239349151793152, 13200984010374774784, 90141957289783853056, 615527786235272626176

S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (see p. 210).

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).

<a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-8).

Empirical gG.f.: -(2*x-1) / (8*x^2-8*x+1). - Colin Barker, Aug 29 20132013a(n) = A057084(n)-2*A057084(n-1). - _R. J. Mathar_, Jul 26 2019

A123357 := proc(n)

option remember;

if n <= 1 then

op(n+1, [1, 6]) ;

else

8*(procname(n-1)-procname(n-2)) ;

end if

end proc:

seq( A123357(n), n=0..30) ; # R. J. Mathar, Jul 26 2019

nonn,easy

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

S. J. Cyvin and I. Gutman, Kekule Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (see p. 210).

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