login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A164391 Number of binary strings of length n with no substrings equal to 0000 or 0111 1
14, 25, 44, 77, 134, 233, 405, 703, 1220, 2117, 3673, 6372, 11054, 19176, 33265, 57705, 100101, 173645, 301221, 522526, 906422, 1572363, 2727565, 4731484, 8207665, 14237766, 24698130, 42843633, 74320480, 128923094, 223641776, 387949454 (list; graph; refs; listen; history; text; internal format)
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 (1,1,1,0,-1,-1).

FORMULA

G.f.: x^4*(-14-11*x-5*x^2+6*x^3+12*x^4+8*x^5)/((1-x)*(x^5+2*x^4+2*x^3+ x^2-1)). - R. J. Mathar, Nov 28 2011

a(n) = 1.6443631... * 1.7346913...^n + O(1), where 1.7346913... is the real root of x^5 - x^3 - 2x^2 - 2x - 1. [Charles R Greathouse IV, Jan 18 2012]

MATHEMATICA

LinearRecurrence[{1, 1, 1, 0, -1, -1}, {14, 25, 44, 77, 134, 233}, 50] (* G. C. Greubel, Sep 18 2017 *)

PROG

(PARI) x='x+O('x^50); Vec(x^4*(-14-11*x-5*x^2+6*x^3+12*x^4+8*x^5)/((1-x)*(x^5+2*x^4+2*x^3+ x^2-1))) \\ G. C. Greubel, Sep 18 2017

CROSSREFS

Sequence in context: A020227 A032608 A164393 * A164392 A164390 A164388

Adjacent sequences:  A164388 A164389 A164390 * A164392 A164393 A164394

KEYWORD

nonn,easy,changed

AUTHOR

R. H. Hardin, Aug 14 2009

EXTENSIONS

Conjectured g.f. verified by Charles R Greathouse IV, Jan 18 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified September 21 15:28 EDT 2017. Contains 292307 sequences.