A123357 Kekulé numbers for certain benzenoids (see the Cyvin-Gutman book for details).

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

Offset: 0

Author

N. J. A. Sloane, Oct 10 2006

Keywords

• nonn
• easy

Links

• S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (see p. 210, formula page 204).
• Index entries for linear recurrences with constant coefficients, signature (8,-8).

Programs

Maple

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

Mathematica

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

Formula

G.f.: -(2*x-1) / (8*x^2-8*x+1). - Colin Barker, Aug 29 2013

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