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A164281
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Triangle read by rows, a Petoukhov sequence (Cf. A164279) generated from (1,2)
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3
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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, 2, 4, 8, 4, 2, 4, 8, 16, 8, 4, 8, 4, 2
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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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 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 10 2009]
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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.
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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.
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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).
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CROSSREFS
| A164279, A164056
A166242 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 10 2009]
Sequence in context: A059149 A186187 A013943 * A082693 A097082 A145173
Adjacent sequences: A164278 A164279 A164280 * A164282 A164283 A164284
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KEYWORD
| nonn,tabl
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 12 2009
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