OFFSET
0,2
COMMENTS
a(n) is also the number of length n ternary words with at least 6 0-digits between any other digits.
The compositions of n in which each natural number is colored by one of p different colors are called p-colored compositions of n. For n>=13, 3*a(n-13) equals the number of 3-colored compositions of n with all parts >=7, such that no adjacent parts have the same color. - Milan Janjic, Nov 27 2011
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,2).
FORMULA
G.f.: 1/(x^6*(1-x-2*x^7)).
a(n) = 2n+1 if n<=7, else a(n) = a(n-1) + 2a(n-7). - Milan Janjic, Mar 09 2015
MAPLE
a:= proc(k::nonnegint) local n, i, j; if k=0 then unapply(3^n, n) else unapply((Matrix(k+1, (i, j)-> if (i=j-1) or j=1 and i=1 then 1 elif j=1 and i=k+1 then 2 else 0 fi)^(n+k))[1, 1], n) fi end(6): seq(a(n), n=0..58);
MATHEMATICA
Series[1/(1-x-2*x^7), {x, 0, 58}] // CoefficientList[#, x]& // Drop[#, 6]& (* Jean-François Alcover, Feb 13 2014 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Aug 16 2008
STATUS
approved