A164397 Number of binary strings of length n with no substrings equal to 0001 or 0111.

1, 2, 4, 8, 14, 24, 41, 68, 112, 184, 300, 488, 793, 1286, 2084, 3376, 5466, 8848, 14321, 23176, 37504, 60688, 98200, 158896, 257105, 416010, 673124, 1089144, 1762278, 2851432, 4613721, 7465164, 12078896, 19544072, 31622980, 51167064, 82790057, 133957134

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..2000 (first 500 terms from R. H. Hardin)

Index entries for linear recurrences with constant coefficients, signature (2,0,0,-2,0,1).

Formula

G.f.: -1/((x^2+x+1)*(x^2+x-1)*(x-1)^2). - R. J. Mathar, Nov 30 2011

Mathematica

LinearRecurrence[{2, 0, 0, -2, 0, 1}, {14, 24, 41, 68, 112, 184}, 40] (* Harvey P. Dale, Jan 23 2012 *)
CoefficientList[Series[-1 (14 - 4 x - 7 x^2 - 14 x^3 + 4 x^4 + 8 x^5) / ((1 + x + x^2) (x^2 + x - 1) (x - 1)^2), {x, 0, 33}], x] (* Vincenzo Librandi, Sep 19 2017 *)

Prog

(PARI) x='x+O('x^50); Vec(-x^4*(14-4*x-7*x^2-14*x^3+4*x^4+8*x^5)/( (1+x+x^2)*(x^2+x-1)*(x-1)^2 )) \\ G. C. Greubel, Sep 18 2017
(Magma) I:=[14, 24, 41, 68, 112, 184]; [n le 6 select I[n] else 2*Self(n-1)-2*Self(n-4)+Self(n-6): n in [1..40]]; // Vincenzo Librandi, Sep 19 2017

Crossrefs

Cf. A178982.

Sequence in context: A182747 A164406 A178982 * A164174 A164396 A164400

Adjacent sequences: A164394 A164395 A164396 * A164398 A164399 A164400

Keyword

nonn,easy

Author

R. H. Hardin, Aug 14 2009

Extensions

Edited by Alois P. Heinz, Oct 27 2017

Status

approved