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A164308
Triangle read by rows, binomial distribution of the terms (1, 3, 9, 27, ...).
2
1, 1, 3, 1, 3, 9, 3, 1, 3, 9, 3, 9, 27, 9, 3, 1, 3, 9, 3, 9, 27, 9, 3, 9, 27, 81, 27, 9, 27, 9, 3, 1, 3, 9, 3, 9, 27, 9, 3, 9, 27, 81, 27, 9, 27, 9, 3
OFFSET
0,3
COMMENTS
Row sums = powers of 4: (1, 4, 16, 64, ...); equivalent to the statement that binomial transform of powers of 3 = powers of 4.
The algorithm converts a set of distinct terms into a binomial distribution of the same terms (given no repeats, initial sequence has terms increasing in magnitude); e.g. row 3 is composed of the terms (1, 3, 9, 27) in a binomial frequency of one 27, three 9's, three 3's and one 1.
FORMULA
Superimpose A164056 by positions over A164308. Next term of A164308 going to the right by rows = 3*(current term of A164308) if corresponding term of A164056 = 1. If 0, next term of A164308 = (1/3) current term.
EXAMPLE
First few rows of A164056:
0;
0, 1;
0, 1, 1, 0;
0, 1, 1, 0, 1, 1, 0, 0;
0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0;
...
Example, row 3. Write row 3 of A164056 on top of row 3, A164308:
(0, 1, 1, 0, 1, 1, 0, 0); generates:
(1, 3, 9, 3, 9, 27, 9, 3)
.
First few rows of A164308:
1;
1, 3;
1, 3, 9, 3;
1, 3, 9, 3, 9, 27, 9, 3;
1, 3, 9, 3, 9, 27, 9, 3, 9, 27, 81, 27 9, 27, 9, 3;
...
CROSSREFS
Cf. A164056.
Sequence in context: A376499 A248830 A350562 * A082511 A265307 A133579
KEYWORD
nonn,tabl,more
AUTHOR
Gary W. Adamson, Aug 12 2009
STATUS
approved