A123348 Kekulé numbers for certain benzenoids (see the Cyvin-Gutman book for details).

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

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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