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.
A(n, k) = 2^(A088696(n+1, k)-1). - Andrey Zabolotskiy, Feb 18 2025
EXAMPLE
MATHEMATICA
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Gary W. Adamson, Aug 12 2009
EXTENSIONS
Corrected and more terms from Jon Maiga, Oct 04 2019
STATUS
approved