OFFSET
0,2
COMMENTS
a(n) is also the number of length n quaternary words with at least 9 0-digits between any other digits.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,3).
FORMULA
G.f.: 1/(x^9*(1-x-3*x^10)).
MAPLE
a := proc(k::nonnegint) local n, i, j; if k=0 then unapply (4^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 3 else 0 fi)^(n+k))[1, 1], n) fi end(9): seq (a(n), n=0..61);
MATHEMATICA
Series[1/(1-x-3*x^10), {x, 0, 61}] // CoefficientList[#, x]& // Drop[#, 9]& (* Jean-François Alcover, Feb 13 2014 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Aug 16 2008
STATUS
approved