0,3

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 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 10 2009]

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.

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.

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).

A164279, A164056

A166242 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 10 2009]

Sequence in context: A059151 A059149 A013943 this_sequence A082693 A097082 A145173

Adjacent sequences: A164278 A164279 A164280 this_sequence A164282 A164283 A164284

nonn,tabl

Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 12 2009