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A164408
Number of binary strings of length n with no substrings equal to 0000 0001 or 0011.
3
1, 2, 4, 8, 13, 23, 40, 68, 118, 203, 349, 602, 1036, 1784, 3073, 5291, 9112, 15692, 27022, 46535, 80137, 138002, 237652, 409256, 704773, 1213679, 2090056, 3599252, 6198214, 10673843, 18381253, 31654058, 54510940, 93872408, 161656153, 278385443, 479403064
OFFSET
0,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..2000 (500 terms from R. H. Hardin)
FORMULA
G.f.: (x+1)*(x^2+1) / ( 1-x-x^2-x^3+x^4 ). - R. J. Mathar, Nov 28 2011
MATHEMATICA
CoefficientList[Series[(13 + 10*x + 4*x^2 - 8*x^3)/(1 - x - x^2 - x^3 + x^4), {x, 0, 50}], x] (* Wesley Ivan Hurt, Jan 10 2017 *)
LinearRecurrence[{1, 1, 1, -1}, {13, 23, 40, 68}, 50] (* G. C. Greubel, Sep 19 2017 *)
PROG
(PARI) x='x+O('x^50); Vec(x^4*(13+10*x+4*x^2-8*x^3)/(1-x-x^2-x^3+x^4)) \\ G. C. Greubel, Sep 19 2017
CROSSREFS
Sequence in context: A164417 A258600 A227232 * A303852 A096573 A348574
KEYWORD
nonn,easy
AUTHOR
R. H. Hardin, Aug 14 2009
EXTENSIONS
Edited by Alois P. Heinz, Dec 30 2023
STATUS
approved