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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A102396 A mod 2 related Jacobsthal sequence. 2
0, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 1, 3, 3, 5, 1, 1, 1, 3, 1, 3, 3, 5, 1, 3, 3, 5, 3, 5, 5, 11, 1, 1, 1, 3, 1, 3, 3, 5, 1, 3, 3, 5, 3, 5, 5, 11, 1, 3, 3, 5, 3, 5, 5, 11, 3, 5, 5, 11, 5, 11, 11, 21, 1, 1, 1, 3, 1, 3, 3, 5, 1, 3, 3, 5, 3, 5, 5, 11, 1, 3, 3, 5, 3, 5, 5, 11, 3, 5, 5, 11, 5, 11, 11, 21, 1, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

a(2^n-1)=A001045(n). Conjecture : all elements a(n) are Jacobsthal numbers. A001316(n)=A102395(n)+2*A102396(n).

The conjecture is true since a(n)=A001045(A000120(n)). - Paul Barry, Jan 07 2005

LINKS

Table of n, a(n) for n=0..97.

FORMULA

a(n)=sum{k=0..n, if(mod(n+k, 3)=1, C(n, k) mod 2, 0)}; a(n)=sum{k=0..n, if(mod(n+k, 3)=2, C(n, k) mod 2, 0)}.

a(n)=(1/2)*sum(k=0, n, {F(n+k)*binomial(n, k)} mod 2) where F=A000045; recurrence : a(0)=0 then a(2n)=a(n) and a(2n+1)=2*a(n)+1-2*t(n) where t(n)=A010060(n) is the Thue-Morse sequence - Benoit Cloitre, May 15 2005

CROSSREFS

Sequence in context: A132468 A243915 A090176 * A095960 A316314 A183093

Adjacent sequences:  A102393 A102394 A102395 * A102397 A102398 A102399

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Jan 06 2005

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 24 18:03 EDT 2019. Contains 322430 sequences. (Running on oeis4.)