A164408 Number of binary strings of length n with no substrings equal to 0000 0001 or 0011.

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)

Index entries for linear recurrences with constant coefficients, signature (1,1,1,-1).

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

Adjacent sequences: A164405 A164406 A164407 * A164409 A164410 A164411

Keyword

nonn,easy

Author

R. H. Hardin, Aug 14 2009

Extensions

Edited by Alois P. Heinz, Dec 30 2023

Status

approved