login
A123357
Kekulé numbers for certain benzenoids (see the Cyvin-Gutman book for details).
2
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
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).
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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Oct 10 2006
STATUS
approved