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A164308
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Triangle read by rows, binomial distribution of the terms (1, 3, 9, 27,...)
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2
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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
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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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.
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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.
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EXAMPLE
| First few rows of A164056 =
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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 =
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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;
...
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CROSSREFS
| A164056
Sequence in context: A010282 A119265 A143453 * A082511 A088442 A037095
Adjacent sequences: A164305 A164306 A164307 * A164309 A164310 A164311
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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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