0,3

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.

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.

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;

...

A164056

Sequence in context: A010282 A119265 A143453 this_sequence A082511 A088442 A037095

Adjacent sequences: A164305 A164306 A164307 this_sequence A164309 A164310 A164311

nonn,tabl

Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 12 2009