login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A284125 Number of binary strings w of length n for which s, the longest proper suffix of w that appears at least twice in w, is of length 2. 2
0, 0, 2, 4, 12, 26, 52, 98, 178, 316, 556, 972, 1694, 2950, 5140, 8968, 15676, 27460, 48212, 84844, 149656, 264578, 468780, 832344, 1480860, 2639730, 4714066, 8432938, 15110070, 27115448, 48729252, 87689374, 157998112, 285016412, 514716578, 930499110, 1683776276 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..37.

Lars Blomberg, C# code for computing the terms of A284125

FORMULA

G.f.: 2*x^3*(1 + x^2)*(1 - 4*x + 6*x^2 - 5*x^3 + x^4 + 2*x^5 + 2*x^6 - 2*x^7) / ((1 - x)^2*(1 - x - x^2)*(1 - 2*x + x^2 - x^3)*(1 - x - x^2 - x^3)) (conjectured). - Colin Barker, Jun 07 2017

EXAMPLE

For n = 5 the 12 such strings are {00100,00101,00111,01000,01001,01101} and their binary complements.

CROSSREFS

Cf. A284122.

Sequence in context: A080375 A136253 A266079 * A045678 A236002 A291406

Adjacent sequences:  A284122 A284123 A284124 * A284126 A284127 A284128

KEYWORD

nonn

AUTHOR

Jeffrey Shallit, Mar 20 2017

EXTENSIONS

a(21)-a(37) from Lars Blomberg, Jun 06 2017

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 30 11:58 EDT 2022. Contains 357105 sequences. (Running on oeis4.)