OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
T. Langley, J. Liese, and J. Remmel, Generating Functions for Wilf Equivalence Under Generalized Factor Order, J. Int. Seq. 14 (2011) # 11.4.2.
Index entries for linear recurrences with constant coefficients, signature (3,-2,0,0,-1,1).
FORMULA
G.f.: (1-x+x^5)/(1-3*x+2*x^2+x^5-x^6).
EXAMPLE
a(6) = 63 = 2^6-1, because 100001 is the only binary word of length 6 with not less than 4 0-digits between any pair of consecutive 1-digits.
MAPLE
a:= n-> (Matrix([[2, 1$5]]). Matrix(6, (i, j)-> if i=j-1 then 1 elif j=1 then [3, -2, 0$2, -1, 1][i] else 0 fi)^n)[1, 2]: seq(a(n), n=0..40);
MATHEMATICA
CoefficientList[Series[(1 - x + x^5) / (1 - 3 x + 2 x^2 + x^5 - x^6), {x, 0, 50}], x] (* Vincenzo Librandi, Jun 06 2013 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Oct 02 2008
STATUS
approved