OFFSET
0,3
COMMENTS
For n>=1, a(n) is the number of words of length n-1 over the alphabet {1,2,3,4,5} such that no two even numbers appear consecutively. - Armend Shabani, Mar 01 2017
LINKS
FORMULA
G.f.: (1 - 2*x - 4*x^2)/(1 - 3*x - 6*x^2).
a(n+1) = Sum_{k=0..n} A154929(n,k)*2^(n-k).
G.f.: Q(0)/6 +2/3 , where Q(k) = 1 + 1/(1 - x*(6*k+3 + 6*x )/( x*(6*k+6 + 6*x ) + 1/Q(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Sep 21 2013
a(n) = A083858(n+1)/3, n>=1. - R. J. Mathar, Feb 06 2020
MATHEMATICA
{1}~Join~LinearRecurrence[{3, 6}, {1, 5}, 25] (* or *)
CoefficientList[Series[(1 - 2 x - 4 x^2)/(1 - 3 x - 6 x^2), {x, 0, 25}], x] (* Michael De Vlieger, Mar 02 2017 *)
PROG
(PARI) Vec((1-2*x-4*x^2)/(1-3*x-6*x^2)+O(x^99)) \\ Charles R Greathouse IV, Jan 11 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Philippe Deléham, Jan 18 2009
STATUS
approved