A164308 Triangle read by rows, binomial distribution of the terms (1, 3, 9, 27, ...).

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

Author

Gary W. Adamson, Aug 12 2009

Keywords

• nonn
• tabl
• more

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.

Examples

			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.

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.