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
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;
...
(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
KEYWORD
AUTHOR
Gary W. Adamson, Aug 12 2009
STATUS
approved