OFFSET
0,2
COMMENTS
Appears to be Kekulé numbers for certain benzenoids (see the Cyvin-Gutman book for details).
REFERENCES
S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (see p. 78).
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..500
D. Birmajer, J. B. Gil, and M. D. Weiner, On the Enumeration of Restricted Words over a Finite Alphabet, J. Int. Seq. 19 (2016) # 16.1.3, example 17.
Index entries for linear recurrences with constant coefficients, signature (4, 2).
FORMULA
From Klaus Brockhaus, Oct 03 2009: (Start)
Inverse binomial transform of A138395.
a(n) = ((2+sqrt(6))^(n+1) + (2-sqrt(6))^(n+1))/4.
a(n) = 4*a(n-1) + 2*a(n-2) for n > 1.
G.f.: (1 + x)/(1 - 4*x - 2*x^2).
(End)
EXAMPLE
a(2) = 22 because all 25 words of length 2 are included except 11, 13 and 15.
MAPLE
seq(coeff(series((1+x)/(1-4*x-2*x^2), x, n+1), x, n), n = 0 .. 25); # Muniru A Asiru, Nov 27 2018
MATHEMATICA
LinearRecurrence[{4, 2}, {1, 5}, 30] (* Amiram Eldar, Nov 26 2018 *)
PROG
(PARI) Vec((1 + x)/(1 - 4*x - 2*x^2) + O(x^30)) \\ Andrew Howroyd, Nov 25 2018
(Magma) I:=[1, 5]; [n le 2 select I[n] else 4*Self(n-1) + 2*Self(n-2): n in [1..30]]; // G. C. Greubel, Nov 29 2018
(Sage) s=((1+x)/(1-4*x-2*x^2)).series(x, 50); s.coefficients(x, sparse=False) # G. C. Greubel, Nov 29 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Oct 10 2006
EXTENSIONS
Edited and new name by Armend Shabani and Andrew Howroyd, Nov 25 2018
STATUS
approved