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

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A117940 a(0)=1, thereafter a(3n) = a(3n+1)/3 = a(n), a(3n+2)=0. 19

%I

%S 1,3,0,3,9,0,0,0,0,3,9,0,9,27,0,0,0,0,0,0,0,0,0,0,0,0,0,3,9,0,9,27,0,

%T 0,0,0,9,27,0,27,81,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,

%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,9,0,9,27,0,0,0,0,9,27,0,27,81,0,0,0,0,0,0

%N a(0)=1, thereafter a(3n) = a(3n+1)/3 = a(n), a(3n+2)=0.

%C a(n) = a(3n)/a(0) = a(3n+1)/a(1). a(n) mod 2 = A039966(n). Row sums of A117939.

%C Observation: if this is written as a triangle (see example) then at least the first five row sums coincide with A002001. - Omar E. Pol, Nov 28 2011

%H David Applegate, Omar E. Pol and N. J. A. Sloane, <a href="http://neilsloane.com/doc/tooth.pdf">The Toothpick Sequence and Other Sequences from Cellular Automata</a>, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]

%H N. J. A. Sloane, <a href="/wiki/Catalog_of_Toothpick_and_CA_Sequences_in_OEIS">Catalog of Toothpick and Cellular Automata Sequences in the OEIS</a>

%F G.f.: Product{k>=0, 1+3x^(3^k)}; a(n)=sum{k=0..n, sum{j=0..n, L(C(n,j)/3)*L(C(n-j,k)/3)}} where L(j/p) is the Legendre symbol of j and p.

%e Contribution from Omar E. Pol, Nov 26 2011 (Start):

%e When written as a triangle this begins:

%e 1,

%e 3,0,

%e 3,9,0,0,0,0,

%e 3,9,0,9,27,0,0,0,0,0,0,0,0,0,0,0,0,0,

%e 3,9,0,9,27,0,0,0,0,9,27,0,27,81,0,0,0,0,0,0,0,0,0,0,0,...

%e (End)

%Y For generating functions Prod_{k>=0} (1+a*x^(b^k)) for the following values of (a,b) see: (1,2) A000012 and A000027, (1,3) A039966 and A005836, (1,4) A151666 and A000695, (1,5) A151667 and A033042, (2,2) A001316, (2,3) A151668, (2,4) A151669, (2,5) A151670, (3,2) A048883, (3,3) A117940, (3,4) A151665, (3,5) A151671, (4,2) A102376, (4,3) A151672, (4,4) A151673, (4,5) A151674.

%K easy,nonn,tabf

%O 0,2

%A _Paul Barry_, Apr 05 2006

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 January 17 14:12 EST 2019. Contains 319225 sequences. (Running on oeis4.)