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

 

Logo

Invitation: celebrating 50 years of OEIS, 250000 sequences, and Sloane's 75th, there will be a conference at DIMACS, Rutgers, Oct 9-10 2014.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A169689 (A169648(4n+4) - A147582(4n+5))/4. 4
0, 1, 6, 4, 24, 4, 20, 12, 84, 4, 20, 12, 76, 12, 60, 36, 276, 4, 20, 12, 76, 12, 60, 36, 260, 12, 60, 36, 228, 36, 180, 108, 876, 4, 20, 12, 76, 12, 60, 36, 260, 12, 60, 36, 228, 36, 180, 108, 844, 12, 60, 36, 228, 36, 180, 108, 780, 36, 180, 108, 684, 108, 540, 324, 2724, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,3

COMMENTS

A169648 and A147582 agree except at these terms.

LINKS

Table of n, a(n) for n=-1..64.

David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata

N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

FORMULA

a(-1)=0, a(0)=1, a(1)=6. For n >= 2, let n = 2^k+j with 0 <= j < 2^k, and write j+1 = 2^m*(2t+1). Then a(n) = 4*(3^(m+1)-2^(m+1))*3^wt(t), except if j=2^k-1 we must add 2^(k+1) to the result (here wt(t) = A000120(t)).

Recurrence: a(-1)=0, a(0)=1, a(1)=6. For n>=2, write n = 2^k + j, with 0 <= j < 2^k. If j+1 is a power of 2, say j+1 = 2^r, set f=j+1 if r<k, f=3(j+1) if r=k, and otherwise set f=0. Then a(n) = 3*a(j) + f. (The explicit formula in the previous line is better.)

Since there is a simple explicit formula for A147582(n), this provides a simple way to generate A169648.

EXAMPLE

Can be written in the form of a triangle:

0,

1,

6,

4,24,

4,20,12,84,

4,20,12,76,12,60,36,276,

4,20,12,76,12,60,36,260,12,60,36,228,36,180,108,876,

4,20,12,76,12,60,36,260,12,60,36,228,36,180,108,844,12,60,36,228,36,180,108,780,36,180,108,684,108,540,324,2724,

...

MAPLE

a:=proc(n) option remember; local f, j, k, t1;

if n=-1 then RETURN(0); elif n=0 then RETURN(1); elif n=1 then RETURN(6);

else k:=floor(log(n)/log(2)); j:=n-2^k; t1 := 2^floor(log(j+1)/log(2));

if t1=j+1 and j < 2^k-1 then f := j+1 elif t1=j+1 then f := 3*(j+1) else f := 0; fi;

RETURN(3*a(j)+f);

fi;

end;

[seq(a(n), n=-1..200)];

CROSSREFS

Equals A169688/4. Cf. A169697 (limit of rows).

Sequence in context: A185734 A120462 A236602 * A061592 A081631 A137174

Adjacent sequences:  A169686 A169687 A169688 * A169690 A169691 A169692

KEYWORD

nonn,tabf

AUTHOR

N. J. A. Sloane, Apr 14 2010

STATUS

approved

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

Content is available under The OEIS End-User License Agreement .

Last modified July 31 13:31 EDT 2014. Contains 245085 sequences.