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!)
A164363 The number of 1's in the n-th stage of A164349 4
1, 1, 2, 3, 6, 12, 23, 46, 91, 182, 364, 727, 1454, 2908, 5816, 11631, 23262, 46523, 93046, 186092, 372183, 744366, 1488732, 2977463, 5954926, 11909851, 23819702, 47639404, 95278807, 190557614, 381115228, 762230456, 1524460911, 3048921822, 6097843643 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
A164349 is generated as follows. Start with the string 01, and at each stage copy the previous string twice and remove the last symbol.
Since the number of symbols in the whole string is 2^n + 1, A164363 + A164362 = 2^n + 1.
LINKS
FORMULA
A recurrence is given in terms of A164364(n) = A164349(2^n):
a(n+1) = 2*a(n) - A164364(n).
EXAMPLE
01 -> 010 -> 01001 -> 010010100 -> 01001010001001010 etc.
So the number of 1's in the n-th stage is the sequence 1, 1, 2, 3, 6 etc.
MATHEMATICA
t = Nest[ Most@ Flatten@ {#, #} &, {0, 1}, 25]; Table[ Count[ Take[t, 2^n + 1], 1], {n, 0, 25}] (* Robert G. Wilson v, Aug 17 2009 *)
CROSSREFS
Sequence in context: A001630 A293363 A326021 * A306809 A103341 A023675
KEYWORD
nonn
AUTHOR
Jack W Grahl, Aug 14 2009
EXTENSIONS
a(23)-a(26) from Robert G. Wilson v, Aug 17 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 29 11:14 EDT 2024. Contains 371278 sequences. (Running on oeis4.)