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 A123348 Kekulé numbers for certain benzenoids (see the Cyvin-Gutman book for details). 1
 0, 3, 12, 54, 240, 1068, 4752, 21144, 94080, 418608, 1862592, 8287584, 36875520, 164077248, 730060032, 3248394624, 14453698560, 64311583488, 286153731072, 1273238091264, 5665259827200, 25207515491328, 112160581619712, 499057357461504, 2220550593085440, 9880317087264768, 43962369535229952 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (see p. 78, Binet formula page 77). Index entries for linear recurrences with constant coefficients, signature (4,2). FORMULA Conjectured g.f.: 1/(1 - Q(0)) - 1, where Q(k)= 1 - 1/(4^k - 2*x*16^k/(2*x*4^k - 1/(1 + 1/(2*4^k - 8*x*16^k/(4*x*4^k + 1/Q(k+1) ))))); (continued fraction). - Sergei N. Gladkovskii, Apr 13 2013 G.f.: -3*x / (2*x^2+4*x-1). a(n)=3*A090017(n). - Colin Barker, Aug 29 2013 MAPLE A123348 := proc(n)     3*((2+sqrt(6))^n-(2-sqrt(6))^n)/2/sqrt(6) ;     expand(%) ;     simplify(%) ; end proc: seq( A123348(n), n=0..30) ; # R. J. Mathar, Jul 26 2019 CROSSREFS Sequence in context: A329056 A191577 A282901 * A151204 A151205 A151206 Adjacent sequences:  A123345 A123346 A123347 * A123349 A123350 A123351 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Oct 10 2006 STATUS approved

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Last modified July 31 18:30 EDT 2021. Contains 346376 sequences. (Running on oeis4.)