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!)
A164485 Number of binary strings of length n with no substrings equal to 0001, 1000 or 1001. 1
13, 21, 33, 53, 85, 137, 221, 357, 577, 933, 1509, 2441, 3949, 6389, 10337, 16725, 27061, 43785, 70845, 114629, 185473, 300101, 485573, 785673, 1271245, 2056917, 3328161, 5385077, 8713237, 14098313, 22811549, 36909861, 59721409, 96631269 (list; graph; refs; listen; history; text; internal format)
OFFSET
4,1
LINKS
Martin Griffiths, On a Matrix Arising from a Family of Iterated Self-Compositions, Journal of Integer Sequences, 18 (2015), #15.11.8.
FORMULA
G.f.: -x^4*(-13 + 5*x + 9*x^2) / ((x - 1)*(x^2 + x - 1)). - R. J. Mathar, Jan 19 2011
a(n) = 4*Fibonacci(n) + 1. - Bruno Berselli, Jul 26 2017
From Colin Barker, Jul 26 2017: (Start)
a(n) = 1 - (4*(((1 - sqrt(5))/2)^n - ((1 + sqrt(5))/2)^n))/sqrt(5) for n>3.
a(n) = 2*a(n-1) - a(n-3) for n>6.
(End)
PROG
(PARI) Vec(-x^4*(-13 + 5*x + 9*x^2) / ((x - 1)*(x^2 + x - 1)) + O(x^60)) \\ Colin Barker, Jul 26 2017
(Python)
from sympy import fibonacci
def a(n): return 4*fibonacci(n) + 1
print([a(n) for n in range(4, 101)]) # Indranil Ghosh, Jul 26 2017
CROSSREFS
Sequence in context: A164488 A164436 A164498 * A164447 A057200 A164454
KEYWORD
nonn,easy
AUTHOR
R. H. Hardin, Aug 14 2009
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 March 19 03:33 EDT 2024. Contains 370952 sequences. (Running on oeis4.)