OFFSET
0,3
COMMENTS
a(n+1) equals the number of words of length n over {0,1,2,3,4,5,6,7} avoiding 01 and 02. - Milan Janjic, Dec 17 2015
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Tomislav Doslic, Planar polycyclic graphs and their Tutte polynomials, Journal of Mathematical Chemistry, Volume 51, Issue 6, 2013, pp. 1599-1607. See Cor. 3.7(e).
Index entries for linear recurrences with constant coefficients, signature (8, -2).
FORMULA
a(n) = ((4 + sqrt(14))^n - (4 - sqrt(14))^n)/(2*sqrt(14)). - Giorgio Balzarotti, May 28 2011
G.f.: x/(1 - 8x + 2*x^2). - Philippe Deléham, Oct 12 2011
E.g.f.: (1/sqrt(14))*exp(4*x)*sinh(sqrt(14)*x). - G. C. Greubel, Dec 18 2015
MATHEMATICA
LinearRecurrence[{8, -2}, {0, 1}, 50]
PROG
(Magma) I:=[0, 1]; [n le 2 select I[n] else 8*Self(n-1)-2*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Dec 17 2015
(PARI) Vec(1/(1-8*x+2*x^2) + O(x^100)) \\ Altug Alkan, Dec 17 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Joseph Stephan Orlovsky, May 24 2011
STATUS
approved