login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A164281 Triangle read by rows, a Petoukhov sequence (cf. A164279) generated from (1,2). 3
1, 1, 2, 1, 2, 4, 2, 1, 2, 4, 2, 4, 8, 4, 2, 1, 2, 4, 2, 4, 8, 4, 2, 4, 8, 16, 8, 4, 8, 4, 2, 1, 2, 4, 2, 4, 8, 4, 2, 4, 8, 16, 8, 4, 8, 4, 2, 4, 8, 16, 8, 16, 32, 16, 8, 4, 8, 16, 8, 4, 8, 4, 2, 1, 2, 4, 2, 4, 8, 4, 2, 4, 8, 16, 8, 4, 8, 4, 2, 4, 8, 16, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Row sums = powers of 3: (1, 3, 9, 27, 81, ...). A164279 = a Petoukhov sequence generated through analogous principles from (3,2), with row sums = powers of 5.

Essentially, A164281 converts the terms (1,2,4,8,...) into rows with a binomial distribution as to frequency of terms. For example, row 3 has one 1, three 2's, three 4's, and one 8. This property arises due to the origin of the system of codes in A164056 (derived from the Gray code).

A Gray code origin also preserves the "one bit" (in this case, a "one product operation") since in each row, the next term is either twice current term or (1/2) current term.

Rows tend to A166242. [Gary W. Adamson, Oct 10 2009]

REFERENCES

Sergei Petoukhov & Matthew He, "Symmetrical Analysis Techniques for Genetic Systems and Bioinformatics - Advanced Patterns and Applications", IGI Global, 978-1-60566-127-9, October 2009, Chapters 2, 4, and 6.

LINKS

Jon Maiga, Table of n, a(n) for n = 0..1022 (Rows 0..9)

FORMULA

Given row terms of triangle A059268: (1; 1,2; 1,2,4; 1,2,4,8;...) and the digital codes in A164056: (0; 0,1; 0,1,1,0; 0,1,1,0,1,1,0,0;...); beginning with "1" in each row, multiply by 2 to obtain the next term to the right, if the corresponding positional term in A164056 = "1". Divide by 2 if the corresponding A164056 term = 0.

EXAMPLE

First few rows of the triangle =

1;

1, 2;

1, 2, 4, 2;

1, 2, 4, 2, 4, 8, 4, 2;

1, 2, 4, 2, 4, 8, 4, 2, 4, 8, 16, 8, 4, 8, 4, 2;

...

Example: row 3 of A164056 =

(0, 1, 1, 0, 1, 1, 0, 0), so beginning with "1" at left, row 3 of A164281 = (1, 2, 4, 2, 4, 8, 4, 2).

MATHEMATICA

A088696[n_]:=A088696[n]=Flatten[NestList[Join[#, Reverse[#]+1]&, {1}, 15]][[n]];

A164281[0]=1;

A164281[n_]:=If[IntegerQ[Log2[n+1]], 1, If[A088696[n+1]>A088696[n], 2*A164281[n-1], A164281[n-1]/2]]

Array[A164281, 100, 0] (* Jon Maiga, Oct 04 2019 *)

CROSSREFS

Cf. A088696, A164279, A164056.

Cf. A166242 [Gary W. Adamson, Oct 10 2009]

Sequence in context: A273917 A186187 A013943 * A082693 A225081 A307368

Adjacent sequences:  A164278 A164279 A164280 * A164282 A164283 A164284

KEYWORD

nonn,tabf

AUTHOR

Gary W. Adamson, Aug 12 2009

EXTENSIONS

Corrected and more terms from Jon Maiga, Oct 04 2019

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 July 26 17:37 EDT 2021. Contains 346294 sequences. (Running on oeis4.)