A164279 -id:A164279 - cp's OEIS frontend

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

Offset: 0

Gary W. Adamson, Aug 12 2009

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

			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).

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.

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

Cf. A088696, A164279, A164056.

Cf. A166242.

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 *)

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.

A(n, k) = 2^(A088696(n+1, k)-1). - Andrey Zabolotskiy, Feb 18 2025

Corrected and more terms from Jon Maiga, Oct 04 2019

cp's OEIS Frontend

A164281 Triangle read by rows, a Petoukhov sequence (cf. A164279) generated from (1,2).

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