A164426 Number of binary strings of length n with no substrings equal to 0000 0011 or 0101.

13, 21, 34, 53, 81, 124, 188, 282, 422, 630, 936, 1387, 2053, 3033, 4473, 6591, 9704, 14274, 20983, 30832, 45283, 66481, 97576, 143181, 210054, 308108, 451874, 662642, 971620, 1424557, 2088498, 3061702, 4488192, 6579052, 9643637, 14135346

Offset

4,1

Links

R. H. Hardin, Table of n, a(n) for n=4..500

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

Formula

G.f.: -x^4*(-13-8*x-13*x^2+7*x^3+14*x^4+12*x^5+8*x^6) / ( (x^3+x-1)*(x^4+x^3-1) ). - R. J. Mathar, Dec 01 2011

a(n) = a(n-1) + 2*a(n-3) - a(n-5) - a(n-6) - a(n-7). - Wesley Ivan Hurt, Aug 19 2022

Mathematica

LinearRecurrence[{1, 0, 2, 0, -1, -1, -1}, {13, 21, 34, 53, 81, 124, 188}, 40] (* Harvey P. Dale, Feb 06 2019 *)

Crossrefs

Sequence in context: A164447 A057200 A164454 * A164473 A164481 A164433

Adjacent sequences: A164423 A164424 A164425 * A164427 A164428 A164429

Keyword

nonn

Author

R. H. Hardin, Aug 14 2009

Status

approved