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

0,2

Links

Table of n, a(n) for n=0..22.

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).

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

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 *)

Crossrefs

Sequence in context: A122074 A289208 A244253 * A081016 A083426 A122471

Adjacent sequences: A123354 A123355 A123356 * A123358 A123359 A123360

Keyword

nonn,easy

Author

N. J. A. Sloane, Oct 10 2006

Status

approved